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3x3_inst24_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 2: Place piece D with its upper-left corner at (x, y) = (1, 1).
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_part/3x3_inst24perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_part/3x3_inst24perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_part/3x3_inst24perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_part/3x3_inst24perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_part/3x3_inst24perturbed_part_assembly_step_4.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (2, 2).", "Place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.2714532942394723, 0.8400670830912441, 0.3547580632505397]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 1, 2], "color": [0.43161052549220547, 0.21272949803204355, 0.15035892470859946]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.7128663156774877, 0.20321597181862183, 0.6465282105669317]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3668565042280403, 0.7544321568579433, 0.022670156613330716]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst18_var1_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 4: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_part/3x3_inst18perturbed_part_assembly_step_4.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.010600729886533378, 0.8500375523210303, 0.41713905454049915]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
3x3_inst0_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "cell_center": [2.049038105676658, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "cell_center": [6.147114317029974, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.8422134984480056, 0.15250547228228883, 0.5324273953128456], "cell_center": [2.049038105676658, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
3x3_inst29_var1_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Place piece A with its lower-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 90, "flip": "none", "color": [0.5587780227736063, 0.37341366971430356, 0.25392528265228476], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.16908974540263644, 0.9028171146233334, 0.20691211710600244], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n111\n001\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
4x4_inst28_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Place piece B with its upper-left corner at (x, y) = (2, 4).
<image_2>
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
<image_3>
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst28/assembly/4x4_inst28assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/assembly/4x4_inst28assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/assembly/4x4_inst28assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/assembly/4x4_inst28assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/assembly/4x4_inst28assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.31870027151465274, 0.9820788726257209, 0.8550947462305866], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.3088457752297562, 0.9442534400895921, 0.6030597092417792], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.2615618203446515, 0.30219545939699477, 0.7851313753013661], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9709321163056576, 0.9638050814682778, 0.48474678634569257], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst13_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_2>
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_3>
Step 4: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst13/assembly/3x3_inst13assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/assembly/3x3_inst13assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/assembly/3x3_inst13assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/assembly/3x3_inst13assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst13/assembly/3x3_inst13assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.5025023117046901, 0.20679137664564085, 0.35368716180716764], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.4167436538845991, 0.3774938048911445, 0.3463506332117947], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.45262734202882937, 0.5605337595606488, 0.8098850090862545], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4122246781876865, 0.46099712359888834, 0.029808170513958232], "cell_center": [5.598076211353316, 1.8660254037844386]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst38_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).
<image_1>
Step 2: Place piece A with its lower-left corner at (x,y) = (-1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).", "Place piece A with its lower-left corner at (x,y) = (-1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 60, "flip": "none", "color": [0.2640373819201658, 0.23801220505274123, 0.0902448886427546], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "none", "color": [0.8335762701827948, 0.8840202519453446, 0.5496566700702556], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n100\n100\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst16_var4_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 4: Place piece C with its upper-left corner at (x, y) = (1, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_step/3x3_inst16perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece C with its upper-left corner at (x, y) = (1, 1)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7676425093614947, 0.24713964046947057, 0.3655219928054467], "cell_center": [1.6160254037844386, 4.5]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9976490339368843, 0.4943065670172001, 0.5594239487418055], "cell_center": [4.848076211353316, 4.5]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.9048699719372921, 0.07001798964152184, 0.5974823649881674], "cell_center": [1.6160254037844386, 1.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.10823406854150919, 0.5033344127325038, 0.9895981043015385], "cell_center": [4.848076211353316, 1.5]}], "variant": "perturbed_step"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst13_var2_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_3>
Step 4: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
<image_4>
Step 5: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2).
<image_5>
Step 6: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
<image_6>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_step/4x4_inst13perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2805251122858946, 0.9715538225079458, 0.3810974789090861], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.7966424419178151, 0.9680914967906663, 0.866954291693426], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.08091420612656075, 0.9562651224873678, 0.23051757819828445], "cell_center": [9.330127018922193, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.13663939469484443, 0.7631849020052232, 0.6462586504062603], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 5, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.29384131363027277, 0.3163325797949277, 0.007829642754902055], "cell_center": [5.598076211353316, 1.8660254037844386]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.9400983497113293, 0.32605090347507637, 0.5045925067978794], "cell_center": [9.330127018922193, 1.8660254037844386]}], "variant": "perturbed_step"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst12_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_2>
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/assembly/3x3_inst12assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/assembly/3x3_inst12assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/assembly/3x3_inst12assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/assembly/3x3_inst12assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/assembly/3x3_inst12assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7158111525953443, 0.3144750396327004, 0.9033798732112359], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868], "cell_center": [5.598076211353316, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
4x4_inst19_var2_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
<image_1>
Step 2: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_3>
Step 4: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
<image_4>
Step 5: Place piece D with its upper-left corner at (x, y) = (0, 2).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481]}, {"index": 4, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.15548994568154517, 0.5175640932286619, 0.924036957862598]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [2, 4, 0, 3], "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n11\n\nPiece E:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst9_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 3).
Step 2: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).
Step 3: Rotate piece B by about 30 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 3).
Step 4: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 1).
<image_1>
Step 5: Place piece E with its upper-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/irregular_assembly/4x4_inst9irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 3).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 1).", "Place piece E with its upper-left corner at (x,y) = (1, 4)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 3, 4], "angle": 30, "flip": "none", "color": [0.08568095338134385, 0.6682948586606138, 0.6055837889275328], "is_merged": false}, {"index": 2, "shape": [1, 3, 2, 4], "angle": 30, "flip": "none", "color": [0.32195261495336813, 0.6322591244083937, 0.7762269388570919], "is_merged": false}, {"index": 1, "shape": [3, 4, 1, 4], "angle": 30, "flip": "none", "color": [0.6391948573912559, 0.6949802608182306, 0.21433155875468102], "is_merged": true}, {"index": 0, "shape": [1, 4, 0, 1], "angle": 90, "flip": "none", "color": [0.3767840683317317, 0.9804349782325034, 0.6211477157651492], "is_merged": false}, {"index": 4, "shape": [[1, 3, 1, 2], [0, 1, 0, 3]], "angle": 0, "flip": "none", "color": [0.726034657723742, 0.14100632109447608, 0.1515951180124674], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n010\n010\n111\n\nPiece C:\n11\n11\n\nPiece D:\n1\n\nPiece E:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst23_var4_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_2>
Step 3: Place piece D with its upper-left corner at (x, y) = (0, 2).
<image_3>
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
<image_4>
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
<image_5>
Step 6: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 2)."], "results": ["", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693], "cell_center": [9.330127018922195, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
3x3_inst2_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_2>
Step 3: Place piece B with its upper-left corner at (x, y) = (0, 2).
<image_3>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_step/3x3_inst2perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_step/3x3_inst2perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_step/3x3_inst2perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_step/3x3_inst2perturbed_step_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.20573163102149872, 0.7110069434915763, 0.3696499764946295], "cell_center": [2.0, 4.5]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "cell_center": [6.0, 4.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "cell_center": [2.0, 1.5]}], "variant": "perturbed_step"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst0_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (4, 2).
<image_1>
Step 5: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_step/4x4_inst0perturbed_step_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (4, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.7898276832817946, 0.4878925327916963, 0.09710359553248094], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst5_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 3).
<image_1>
Step 2: Place piece A with its upper-left corner at (x,y) = (0, 1).
<image_2>
Step 3: Rotate piece G by about 30 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (2, 4).
<image_3>
Step 4: Place piece B with its upper-left corner at (x,y) = (1, 1).
<image_4>
Step 5: Rotate piece F by about 60 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (0, 4).
<image_5>
Step 6: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 1).
<image_6>
Step 7: Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 3).
<image_7>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_7.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 3).", "Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece G by about 30 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (2, 4).", "Place piece B with its upper-left corner at (x,y) = (1, 1).", "Rotate piece F by about 60 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 1).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 0, 1], "angle": 30, "flip": "none", "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 2], "angle": 0, "flip": "none", "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437], "is_merged": false}, {"index": 6, "shape": [[3, 4, 0, 2], [1, 3, 0, 1]], "angle": 30, "flip": "none", "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175], "is_merged": false}, {"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333], "is_merged": false}, {"index": 5, "shape": [0, 1, 2, 4], "angle": 60, "flip": "none", "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846], "is_merged": true}, {"index": 2, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061], "is_merged": false}, {"index": 4, "shape": [0, 1, 1, 2], "angle": 60, "flip": "none", "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748], "is_merged": false}], "results": ["", "", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nPiece E:\n1\n\nPiece F:\n11\n10\n10\n\nPiece G:\n11\n10\n10\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst69_var4_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (1, 4).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.8289271958121602, 0.2874252866675162, 0.18696413859663752], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.8091960335687763, 0.16612470580039684, 0.5513661647674789], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst5_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/irregular_assembly/3x3_inst5invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 30, "flip": "none", "color": [0.07357053851548412, 0.9733870202483494, 0.6618987325140707], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 2, 3]], "angle": 0, "flip": "vertical", "color": [0.445111390892756, 0.16653115882702152, 0.8213500363599643], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
4x4_inst29_var3_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).
<image_3>
Step 4: Place piece C with its upper-left corner at (x, y) = (3, 4).
<image_4>
Step 5: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
<image_5>
Step 6: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_part/4x4_inst29perturbed_part_assembly_step_6.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Over board", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924]}, {"index": 4, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [3, 5, 0, 3], "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.6488651399575482, 0.3550425908569148, 0.6083596641075071]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nPiece D:\n111\n\nPiece E:\n11\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
3x3_inst15_var4_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 3).
Step 2: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).
<image_1>
Step 3: Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst15/irregular_assembly/3x3_inst15irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/irregular_assembly/3x3_inst15irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/irregular_assembly/3x3_inst15irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst15/irregular_assembly/3x3_inst15irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [0, 1, 2, 3], "angle": 90, "flip": "none", "color": [0.5860967147337509, 0.19822060430604183, 0.7985991759604419], "is_merged": true}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 90, "flip": "none", "color": [0.910380989877349, 0.7228160858320822, 0.7740539608931295], "is_merged": false}, {"index": 2, "shape": [[1, 3, 1, 3], [0, 1, 0, 2]], "angle": 90, "flip": "none", "color": [0.678651528421504, 0.2548722306191047, 0.7768283693786211], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n110\n111\n001\n\nPiece C:\n110\n111\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst29_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Place piece D with its upper-left corner at (x, y) = (0, 2).
Step 4: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Step 5: Place piece C with its upper-left corner at (x, y) = (3, 4).
<image_1>
Step 6: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/perturbed_step/4x4_inst29perturbed_step_assembly_step_6.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece C with its upper-left corner at (x, y) = (3, 4).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "Over board", "Over board", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469], "cell_center": [2.0, 6.0]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924], "cell_center": [6.0, 6.0]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473], "cell_center": [10.0, 6.0]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.6488651399575482, 0.3550425908569148, 0.6083596641075071], "cell_center": [2.0, 2.0]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405], "cell_center": [6.0, 2.0]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212], "cell_center": [10.0, 2.0]}], "variant": "perturbed_step"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
3x3_inst19_var4_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_2>
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
<image_3>
Step 4: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 1).
<image_4>
Step 5: Place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/perturbed_part/3x3_inst19perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 1).", "Place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8415274483290549, 0.46286374035661404, 0.8797592115225641]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.4978586459293345, 0.5976559765313394, 0.14086452934263438]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.8916148044641335, 0.3781423287870871, 0.36352922300777135]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.568589415325386, 0.5333890295436079, 0.9833430947635076]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3223902645479415, 0.8258414522110806, 0.3821764742442382]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n1\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
4x4_inst10_var2_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x,y) = (2, 4).
<image_1>
Step 2: Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its upper-left corner at (x,y) = (0, 3).
<image_2>
Step 3: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).
<image_3>
Step 4: Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).
<image_4>
Step 5: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 1).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/irregular_assembly/4x4_inst10irregular_assembly_step_5.png"], "instructions": ["", "Place piece D with its upper-left corner at (x,y) = (2, 4).", "Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 1)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 2, 4], "angle": 0, "flip": "none", "color": [0.7227327947376154, 0.03867259473351192, 0.7187065902508578], "is_merged": false}, {"index": 2, "shape": [0, 1, 0, 2], "angle": 30, "flip": "vertical", "color": [0.6583796654906042, 0.6756935160824654, 0.35383825296178073], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 2], "angle": 90, "flip": "none", "color": [0.985913636595184, 0.05054811512912383, 0.006039335896045883], "is_merged": false}, {"index": 4, "shape": [[1, 3, 0, 2], [1, 2, 2, 4]], "angle": 30, "flip": "none", "color": [0.25836663280757977, 0.2609931063406825, 0.8704001126195765], "is_merged": false}, {"index": 1, "shape": [2, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.7647943845442875, 0.521793038303051, 0.22931721031735863], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1111\n1100\n\nPiece D:\n11\n\nPiece E:\n1100\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst27_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 30, "flip": "vertical", "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst40_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst40/irregular_assembly/4x4_inst40invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 3], "angle": 60, "flip": "none", "color": [0.9306636850349022, 0.09874831235672099, 0.7356310587347471], "is_merged": false}, {"index": 1, "shape": [[2, 4, 0, 4], [0, 2, 3, 4]], "angle": 30, "flip": "none", "color": [0.45980852671857286, 0.49464127963619375, 0.4191284231456216], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1111\n1111\n0010\n0010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst23_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
<image_2>
Step 3: Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 4).
<image_3>
Step 4: Place piece E with its upper-left corner at (x,y) = (3, 4).
<image_4>
Step 5: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/irregular_assembly/4x4_inst23irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 4).", "Place piece E with its upper-left corner at (x,y) = (3, 4).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 90, "flip": "none", "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872], "is_merged": false}, {"index": 3, "shape": [2, 4, 3, 4], "angle": 90, "flip": "none", "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156], "is_merged": false}, {"index": 2, "shape": [0, 2, 1, 2], "angle": 60, "flip": "none", "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693], "is_merged": true}, {"index": 4, "shape": [[0, 2, 2, 4], [2, 4, 1, 3]], "angle": 0, "flip": "none", "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 90, "flip": "none", "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n\nPiece C:\n110\n110\n011\n011\n\nPiece D:\n11\n\nPiece E:\n110\n110\n011\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst3_var1_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
<image_2>
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).
<image_3>
Step 4: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_4>
Step 5: Rotate piece H by about 60 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).
<image_5>
Step 6: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
<image_6>
Step 7: Place piece F with its upper-left corner at (x, y) = (1, 2).
<image_7>
Step 8: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece H by about 60 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 2).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "cell_center": [1.8660254037844386, 10.24519052838329]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "cell_center": [5.598076211353316, 10.24519052838329]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "cell_center": [9.330127018922193, 10.24519052838329]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "cell_center": [1.8660254037844386, 6.147114317029974]}, {"index": 7, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "cell_center": [9.330127018922193, 6.147114317029974]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "cell_center": [1.8660254037844386, 2.049038105676658]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "cell_center": [5.598076211353316, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
4x4_inst21_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (2, 4).
<image_1>
Step 2: Place piece C with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_3>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "valid": true, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 3, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 3, 2, 4], "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281], "cell_center": [7.5, 6.348076211353316]}, {"index": 2, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.13844656237050856, 0.09373377464750454, 0.41854255601994583], "cell_center": [2.5, 2.116025403784439]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 3, "w": 3.598076211353316, "h": 3.2320508075688776, "label": "2x3", "piece": [0, 3, 0, 2], "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948], "cell_center": [2.5, 6.348076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n11\n11\n11\n\nPiece C:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst0_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_2>
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/assembly/3x3_inst0assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "cell_center": [2.049038105676658, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "cell_center": [6.147114317029974, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.8422134984480056, 0.15250547228228883, 0.5324273953128456], "cell_center": [2.049038105676658, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
3x3_inst11_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
<image_2>
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst11/assembly/3x3_inst11assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.20466808994905894, 0.704066164831489, 0.6231877093078216], "cell_center": [2.0, 4.5]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.10167857717644269, 0.8327584618892119, 0.8500740367164027], "cell_center": [6.0, 4.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.727812832035729, 0.9023721118321468, 0.059719741721927844], "cell_center": [2.0, 1.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
3x3_inst28_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 2).
<image_3>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/perturbed_step/3x3_inst28perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/perturbed_step/3x3_inst28perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/perturbed_step/3x3_inst28perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/perturbed_step/3x3_inst28perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.08038459038445755, 0.7628332166932088, 0.014888669554417922], "cell_center": [2.0, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "cell_center": [6.0, 5.598076211353316]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "cell_center": [2.0, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst14_var4_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Place piece F with its upper-left corner at (x, y) = (3, 2).
<image_1>
Step 6: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_6.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.5631914090172505, 0.5804703370467916, 0.4790988214748605], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.15000823947344966, 0.4439607975953732, 0.1370434408981498], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.6561140073467281, 0.4764433888300178, 0.7238357704859639], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25169887858646867, 0.6011267349617215, 0.9995531297392487], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.8928397408510584, 0.20487579654854826, 0.908916065600491], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.23171741259592205, 0.12354035634812421, 0.9975313433534191], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
3x3_inst29_var1_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Place piece A with its lower-left corner at (x,y) = (1, 4).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst29/irregular_assembly/3x3_inst29invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 90, "flip": "none", "color": [0.5587780227736063, 0.37341366971430356, 0.25392528265228476], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.16908974540263644, 0.9028171146233334, 0.20691211710600244], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n111\n001\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst30_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/irregular_assembly/3x3_inst30invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "none", "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1110\n0011\n0011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst12_var4_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Place piece D with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
<image_3>
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 4, "orig_height": 3, "w": 4.598076211353316, "h": 4.964101615137755, "label": "4x3", "piece": [0, 3, 0, 4], "color": [0.8269286759639897, 0.28853959708119414, 0.11506735623330777]}, {"index": 3, "angle": 60, "orig_width": 4, "orig_height": 1, "w": 2.8660254037844393, "h": 3.9641016151377544, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.8799540670390662, 0.016815702542142485, 0.6851494150554925]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.6933282349034623, 0.28464064197742567, 0.5984440934517744]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.49483518787283254, 0.25660426038958584, 0.4007459306539174]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n1111\n1111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n1\n1\n1\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst10_var0_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).
Step 5: Place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.08300347331815172, 0.9129260346492023, 0.030327958859172166]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 1, 3], "color": [0.6956976668525877, 0.5614724968196306, 0.20881351979388718]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.8361559109194318, 0.10012585524596118, 0.741018254845187]}, {"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.5852133457184661, 0.9478767577739693, 0.225765369032627]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3863759873563767, 0.3560346662754732, 0.9984770026551721]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n1\n1\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst21_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x, y) = (1, 2).
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_part/3x3_inst21perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_part/3x3_inst21perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_part/3x3_inst21perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_part/3x3_inst21perturbed_part_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [1, 4, 1, 4], "color": [0.5750109852621413, 0.4718251861047962, 0.07260160357926093]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.6140362933411411, 0.9726156360309749, 0.23541658483033545]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.6165348490517608, 0.47248907820449537, 0.17394439876786527]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n11\n\nPiece C:\n111\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst72_var1_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "horizontal", "color": [0.8721773622006816, 0.41303145576010014, 0.7791921499016435], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.5908631975774135, 0.17639180955650813, 0.08214364632741677], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst18_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
<image_2>
Step 3: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).
<image_3>
Step 4: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_step/3x3_inst18perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_step/3x3_inst18perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_step/3x3_inst18perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_step/3x3_inst18perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst18/perturbed_step/3x3_inst18perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.11654719097461486, 0.3924294240647598, 0.5378042635188506], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.010600729886533378, 0.8500375523210303, 0.41713905454049915], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.17693734122658056, 0.6003726390211623, 0.25113789613439574], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.21606549856304313, 0.2484660411194164, 0.5092478714383866], "cell_center": [5.598076211353316, 1.8660254037844386]}], "variant": "perturbed_step"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst29_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2).
<image_2>
Step 3: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
<image_3>
Step 4: Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its lower-left corner at (x,y) = (0, 4).
<image_4>
Step 5: Rotate piece E by about 90 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst29/irregular_assembly/4x4_inst29invalid_irregular_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2).", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Flip piece C vertically. Place piece C with its lower-left corner at (x,y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4)."], "results": ["", "", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.5891291035296236, 0.3497096728096557, 0.9163403319569924], "is_merged": false}, {"index": 1, "shape": [0, 2, 1, 3], "angle": 60, "flip": "none", "color": [0.9543183423703964, 0.16273279693061327, 0.4214676188543469], "is_merged": false}, {"index": 3, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.9741545288927297, 0.34746803917361757, 0.23806606283364473], "is_merged": false}, {"index": 2, "shape": [3, 4, 0, 2], "angle": 30, "flip": "vertical", "color": [0.5990452770695724, 0.8191791111282444, 0.6830708139237405], "is_merged": true}, {"index": 4, "shape": [[0, 3, 3, 4], [2, 3, 0, 3]], "angle": 90, "flip": "none", "color": [0.9906664263285482, 0.5961649832123572, 0.09772349038033212], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n0001\n1111\n0001\n\nPiece D:\n11\n\nPiece E:\n111\n100\n100\n100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
3x3_inst48_var4_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 30, "flip": "none", "color": [0.5435938558033044, 0.035507830349890024, 0.4401982331145228], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 30, "flip": "none", "color": [0.30153112752842937, 0.6867856503031506, 0.39580797040893645], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1100\n1100\n0111\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
3x3_inst52_var0_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (-1, 3).
<image_1>
Step 2: Place piece B with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst52/irregular_assembly/3x3_inst52invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst52/irregular_assembly/3x3_inst52invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst52/irregular_assembly/3x3_inst52invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (-1, 3).", "Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 1], "angle": 90, "flip": "horizontal", "color": [0.22446101034322108, 0.7291343888167078, 0.14292682554717273], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 0, "flip": "none", "color": [0.5509235937581919, 0.5311557431484011, 0.6502805239723363], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n001\n001\n111\n110\n\nPiece B:\n011\n011\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
4x4_inst5_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).
<image_1>
Step 2: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 3: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).
Step 4: Place piece D with its upper-left corner at (x, y) = (0, 3).
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 3).
Step 6: Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (2, 1).
Step 7: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).
Step 8: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_step/4x4_inst5perturbed_step_assembly_step_8.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 3).", "Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (2, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "", "Over board", "", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061], "cell_center": [1.8660254037844388, 9.330127018922193]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 1, 2], "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333], "cell_center": [5.598076211353316, 9.330127018922193]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175], "cell_center": [9.330127018922195, 9.330127018922193]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 7, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.48160700821724445, 0.60931785491179, 0.22992601917545952], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 1, 2], "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst10_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Step 2: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 6: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst10/assembly/4x4_inst10assembly_step_6.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.7647943845442875, 0.521793038303051, 0.22931721031735863], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 5, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.20248606624170273, 0.14080963695668047, 0.6747970029148332], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.25836663280757977, 0.2609931063406825, 0.8704001126195765], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 0, 2], "color": [0.985913636595184, 0.05054811512912383, 0.006039335896045883], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.6583796654906042, 0.6756935160824654, 0.35383825296178073], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [1, 2, 2, 4], "color": [0.7227327947376154, 0.03867259473351192, 0.7187065902508578], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n11\n11\n\nPiece F:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst21_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 4).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 2]], "angle": 60, "flip": "horizontal", "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281], "is_merged": true}, {"index": 0, "shape": [0, 3, 2, 4], "angle": 30, "flip": "none", "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1111\n0011\n0011\n0011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst6_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).
<image_1>
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
<image_2>
Step 3: Place piece C with its upper-left corner at (x, y) = (0, 1).
<image_3>
Step 4: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_part/3x3_inst6perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_part/3x3_inst6perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_part/3x3_inst6perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_part/3x3_inst6perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/perturbed_part/3x3_inst6perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [2, 3, 1, 2], "color": [0.6105635106668218, 0.5212834123536789, 0.6078952969319183]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 2, 3], "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.1586208137251468, 0.12393853736495797, 0.8716693278560734]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n\nPiece C:\n111\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst12_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 3).
Step 4: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_step/3x3_inst12perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7158111525953443, 0.3144750396327004, 0.9033798732112359], "cell_center": [1.5, 4.5]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583], "cell_center": [4.5, 4.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868], "cell_center": [1.5, 1.5]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638], "cell_center": [4.5, 1.5]}], "variant": "perturbed_step"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
4x4_inst14_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Place piece F with its upper-left corner at (x, y) = (3, 2).
Step 6: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_6.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.5631914090172505, 0.5804703370467916, 0.4790988214748605], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.15000823947344966, 0.4439607975953732, 0.1370434408981498], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.6561140073467281, 0.4764433888300178, 0.7238357704859639], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25169887858646867, 0.6011267349617215, 0.9995531297392487], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.8928397408510584, 0.20487579654854826, 0.908916065600491], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.23171741259592205, 0.12354035634812421, 0.9975313433534191], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst71_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3).
<image_1>
Step 2: Place piece A with its upper-left corner at (x,y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst71/irregular_assembly/3x3_inst71invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst71/irregular_assembly/3x3_inst71invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst71/irregular_assembly/3x3_inst71invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 60, "flip": "horizontal", "color": [0.6448409765307426, 0.7101669203718958, 0.20865147660769812], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 0, "flip": "none", "color": [0.8515140863735942, 0.06464843085942373, 0.8392680633265187], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n010\n010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst41_var2_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 30, "flip": "vertical", "color": [0.5615163959144739, 0.8754968350575798, 0.9340271731662201], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 60, "flip": "none", "color": [0.6566695133190994, 0.6035193980322114, 0.9422149247873488], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0111\n1100\n1100\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst3_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
<image_2>
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).
<image_3>
Step 4: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_4>
Step 5: Rotate piece H by about 60 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).
Step 6: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
Step 7: Place piece F with its upper-left corner at (x, y) = (1, 2).
Step 8: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_step/4x4_inst3perturbed_step_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece H by about 60 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece F with its upper-left corner at (x, y) = (1, 2).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563], "cell_center": [1.8660254037844386, 10.24519052838329]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813], "cell_center": [5.598076211353316, 10.24519052838329]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002], "cell_center": [9.330127018922193, 10.24519052838329]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004], "cell_center": [1.8660254037844386, 6.147114317029974]}, {"index": 7, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412], "cell_center": [9.330127018922193, 6.147114317029974]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089], "cell_center": [1.8660254037844386, 2.049038105676658]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383], "cell_center": [5.598076211353316, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst14_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_2>
Step 3: Place piece C with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst14/perturbed_part/3x3_inst14perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/perturbed_part/3x3_inst14perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/perturbed_part/3x3_inst14perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst14/perturbed_part/3x3_inst14perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "Over board"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.7375466272024475, 0.7958785429353309, 0.9602750500929624]}, {"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.6986416373362043, 0.39103013274436993, 0.7338256355090964]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 3, "w": 3.0, "h": 3.0, "label": "3x3", "piece": [1, 4, 1, 4], "color": [0.7571710444334083, 0.6145865680611448, 0.2092124857635973]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n1\n1\n\nPiece C:\n111\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst22_var4_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
<image_1>
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_2>
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst22/assembly/3x3_inst22assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/assembly/3x3_inst22assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/assembly/3x3_inst22assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/assembly/3x3_inst22assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/assembly/3x3_inst22assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.7625957197009988, 0.9880404381427733, 0.37197914191274184], "cell_center": [4.5, 4.848076211353316]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.7857756960096848, 0.6067251586117914, 0.34088809144427157], "cell_center": [1.5, 1.6160254037844386]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.8710687100386045, 0.541800756938831, 0.8463220295003806], "cell_center": [1.5, 4.848076211353316]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.8653102169113169, 0.6383200840503016, 0.9372851837319934], "cell_center": [4.5, 1.6160254037844386]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
4x4_inst54_var4_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 4).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst54/irregular_assembly/4x4_inst54invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst54/irregular_assembly/4x4_inst54invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst54/irregular_assembly/4x4_inst54invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 4).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 4, 0, 1], "angle": 60, "flip": "vertical", "color": [0.8726792980167472, 0.891620226757372, 0.8688991741417201], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 4], [1, 4, 1, 4]], "angle": 60, "flip": "none", "color": [0.7586486642602278, 0.11807337394980355, 0.5631878098048986], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11110\n00111\n00111\n00111\n\nPiece B:\n0111\n0111\n0111\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
3x3_inst22_var1_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 1).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_2>
Step 3: Place piece D with its upper-left corner at (x, y) = (1, 2).
<image_3>
Step 4: Place piece B with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst22/perturbed_step/3x3_inst22perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/perturbed_step/3x3_inst22perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/perturbed_step/3x3_inst22perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/perturbed_step/3x3_inst22perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/perturbed_step/3x3_inst22perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece B with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "Over board", "", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.7857756960096848, 0.6067251586117914, 0.34088809144427157], "cell_center": [1.6160254037844386, 4.5]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.8710687100386045, 0.541800756938831, 0.8463220295003806], "cell_center": [4.848076211353316, 4.5]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.8653102169113169, 0.6383200840503016, 0.9372851837319934], "cell_center": [1.6160254037844386, 1.5]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.7625957197009988, 0.9880404381427733, 0.37197914191274184], "cell_center": [4.848076211353316, 1.5]}], "variant": "perturbed_step"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
3x3_inst9_var2_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 3).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst9/irregular_assembly/3x3_inst9irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/irregular_assembly/3x3_inst9irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/irregular_assembly/3x3_inst9irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/irregular_assembly/3x3_inst9irregular_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "valid": true, "config": [{"index": 2, "shape": [[0, 2, 1, 3], [2, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.5491620960992412, 0.8847398297155372, 0.43877106489933393], "is_merged": false}, {"index": 1, "shape": [2, 3, 0, 2], "angle": 30, "flip": "horizontal", "color": [0.1919730202293154, 0.3911833530705978, 0.8454502921977165], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.5904030260647292, 0.1502228379867938, 0.09526647902491858], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n10\n11\n11\n\nPiece C:\n01\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
3x3_inst28_var0_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 60, "flip": "none", "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 60, "flip": "horizontal", "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
4x4_inst9_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_2>
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).
<image_3>
Step 4: Place piece E with its upper-left corner at (x, y) = (2, 3).
<image_4>
Step 5: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
<image_5>
Step 6: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_6>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst9/assembly/4x4_inst9assembly_step_6.png"], "instructions": ["", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece E with its upper-left corner at (x, y) = (2, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 5, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.28340804127686015, 0.9232672116663543, 0.8311037648416407], "cell_center": [10.24519052838329, 2.049038105676658]}, {"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.3767840683317317, 0.9804349782325034, 0.6211477157651492], "cell_center": [2.049038105676658, 6.147114317029974]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 1, 2], "color": [0.08568095338134385, 0.6682948586606138, 0.6055837889275328], "cell_center": [2.049038105676658, 2.049038105676658]}, {"index": 4, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.726034657723742, 0.14100632109447608, 0.1515951180124674], "cell_center": [6.147114317029974, 2.049038105676658]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 3, 4], "color": [0.6391948573912559, 0.6949802608182306, 0.21433155875468102], "cell_center": [6.147114317029974, 6.147114317029974]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [1, 4, 0, 1], "color": [0.32195261495336813, 0.6322591244083937, 0.7762269388570919], "cell_center": [10.24519052838329, 6.147114317029974]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n1\n\nPiece C:\n1\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst30_var1_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (1, 1).
<image_1>
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_2>
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).
<image_4>
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).
<image_5>
Step 6: Place piece B with its upper-left corner at (x, y) = (3, 4).
<image_6>
Step 7: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_7>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (1, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 6, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.3925122716097921, 0.08314977817411329, 0.23188307859675394]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435]}, {"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.05693842955173811, 0.9065171787135644, 0.309832012336156]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n\nPiece G:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst24_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
<image_1>
Step 2: Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).
<image_3>
Step 4: Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 2, "shape": [0, 2, 3, 4], "angle": 60, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 90, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "is_merged": false}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n110\n110\n111\n\nPiece C:\n1\n1\n\nPiece D:\n100\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst17_var2_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 4).
<image_2>
Step 3: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
<image_3>
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).
<image_4>
Step 5: Place piece C with its upper-left corner at (x, y) = (3, 4).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Place piece C with its upper-left corner at (x, y) = (3, 4)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9578521580074713, 0.8815921980787345, 0.19295089472973515], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3209357623770135, 0.4919116750200321, 0.05254088833875614], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.06114350981419958, 0.30119771230277814, 0.1293300317914955], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.09830256447954788, 0.3396191061459677, 0.9867290956314256], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.8024254343287276, 0.5212933415712149, 0.6519422431117098], "cell_center": [9.330127018922195, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nPiece E:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst2_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece E with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 2: Place piece B with its upper-left corner at (x, y) = (2, 4).
<image_2>
Step 3: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 1).
<image_3>
Step 4: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
<image_4>
Step 5: Place piece A with its upper-left corner at (x, y) = (0, 4).
<image_5>
Step 6: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).
Step 7: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/assembly/4x4_inst2assembly_step_7.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3)."], "valid": true, "config": [{"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.4062185845144768, 0.82080352213676, 0.12435592468962808], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6569014157009531, 0.2313466861102611, 0.010872417072518958], "cell_center": [5.598076211353316, 9.330127018922193]}, {"index": 6, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.3036862549445286, 0.2573646344972037, 0.48565653763236827], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 0, 2], "color": [0.6355020062380002, 0.8225754659177894, 0.9905175449642316], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.4909418154450287, 0.8295599853485568, 0.8848537987406436], "cell_center": [1.8660254037844388, 9.330127018922193]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 1, 2], "color": [0.09465920484769241, 0.5230886510184202, 0.29886511441981023], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.5214964160883804, 0.14197386071806894, 0.6150886066496369], "cell_center": [9.330127018922195, 9.330127018922193]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n1\n\nPiece F:\n1\n\nPiece G:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst0_var1_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 2).
<image_1>
Step 5: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst0/perturbed_part/4x4_inst0perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "Over board", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.6587979169912652, 0.844257398556249, 0.15584553214536334]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.6408366795251199, 0.44684470588581293, 0.7884302557046777]}, {"index": 3, "angle": 60, "orig_width": 4, "orig_height": 1, "w": 2.8660254037844393, "h": 3.9641016151377544, "label": "4x1", "piece": [2, 3, 1, 5], "color": [0.4580368292258854, 0.8158453451238444, 0.9632351452602854]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.7898276832817946, 0.4878925327916963, 0.09710359553248094]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.25876504303189696, 0.6936112618438536, 0.14086831103305852]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1111\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst26_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst26/perturbed_step/4x4_inst26perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst26/perturbed_step/4x4_inst26perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst26/perturbed_step/4x4_inst26perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst26/perturbed_step/4x4_inst26perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 3, "w": 3.598076211353316, "h": 3.2320508075688776, "label": "2x3", "piece": [0, 3, 0, 2], "color": [0.2046771522625852, 0.6943746193771417, 0.047460348425434895], "cell_center": [2.299038105676658, 7.446152422706632]}, {"index": 2, "angle": 60, "orig_width": 4, "orig_height": 1, "w": 2.8660254037844393, "h": 3.9641016151377544, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.8108707380944121, 0.2515396058037127, 0.33952569941559574], "cell_center": [6.897114317029974, 7.446152422706632]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 3, "w": 3.0, "h": 2.0, "label": "2x3", "piece": [0, 3, 2, 4], "color": [0.31277665174922176, 0.35495538459548914, 0.3185787817539524], "cell_center": [2.299038105676658, 2.482050807568877]}], "variant": "perturbed_step"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst17_var1_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3).
<image_2>
Step 3: Place piece A with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.5019930741412741, 0.012559332865545225, 0.17639361210978133], "cell_center": [1.5, 4.848076211353316]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.14133289160513685, 0.7931598690282321, 0.18641685245599515], "cell_center": [4.5, 4.848076211353316]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.3661900859965067, 0.7558139235341418, 0.8335971471271846], "cell_center": [1.5, 1.6160254037844386]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.5781587086361871, 0.8308911842343512, 0.6376093319739924], "cell_center": [4.5, 1.6160254037844386]}], "variant": "perturbed_step"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst30_var4_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).
<image_2>
Step 3: Place piece D with its upper-left corner at (x,y) = (0, 4).
<image_3>
Step 4: Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).
<image_4>
Step 5: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 1, 3], "angle": 90, "flip": "none", "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [0, 1, 0, 3]], "angle": 30, "flip": "none", "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "is_merged": false}, {"index": 3, "shape": [3, 4, 1, 4], "angle": 0, "flip": "none", "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "horizontal", "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1000\n1000\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n111\n\nPiece E:\n0001\n0001\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst8_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
<image_2>
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
<image_3>
Step 4: Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).
<image_4>
Step 5: Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (3, 2).
<image_5>
Step 6: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 2).
<image_6>
Step 7: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 8: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_part/4x4_inst8perturbed_part_assembly_step_8.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (3, 2).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368]}, {"index": 7, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.7271419340809824, 0.20886182726939972, 0.6934623432492055]}, {"index": 6, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 3, 4], "color": [0.8441902472414256, 0.8605058939309127, 0.9086859759671123]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n11\n11\n\nPiece G:\n11\n\nPiece H:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst23_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_2>
Step 3: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 5: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 6: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_6.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693], "cell_center": [7.5, 4.848076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872], "cell_center": [1.5, 4.848076211353316]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304], "cell_center": [7.5, 1.6160254037844386]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298], "cell_center": [4.5, 4.848076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156], "cell_center": [1.5, 1.6160254037844386]}, {"index": 4, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927], "cell_center": [4.5, 1.6160254037844386]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst27_var0_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/assembly/4x4_inst27assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 2, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797], "cell_center": [2.549038105676658, 2.549038105676658]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253], "cell_center": [2.549038105676658, 7.647114317029974]}, {"index": 1, "angle": 30, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028], "cell_center": [7.647114317029974, 7.647114317029974]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n111\n111\n111\n\nPiece C:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
3x3_inst26_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8601757328506661, 0.8373920802150087, 0.4098927320047637], "cell_center": [6.147114317029974, 5.049038105676658]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.769985114119021, 0.6023151000208017, 0.43905466192464926], "cell_center": [2.049038105676658, 1.6830127018922192]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.1762969342918307, 0.2700538547336413, 0.9959210428826512], "cell_center": [2.049038105676658, 5.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst21_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4).
<image_1>
Step 2: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/irregular_assembly/4x4_inst21invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 2]], "angle": 60, "flip": "horizontal", "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281], "is_merged": true}, {"index": 0, "shape": [0, 3, 2, 4], "angle": 90, "flip": "none", "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1111\n0110\n0110\n0110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst27_var4_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Place piece B with its upper-left corner at (x, y) = (1, 3).
<image_2>
Step 3: Place piece D with its upper-left corner at (x, y) = (0, 1).
<image_3>
Step 4: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
<image_4>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912]}, {"index": 3, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.08831913378263734, 0.050174014729534866, 0.27620176775171223]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.7341641971685425, 0.29244769077896215, 0.1293027898421113]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
3x3_inst0_var1_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).
<image_2>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 60, "flip": "vertical", "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n0011\n0011\n1110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst30_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_step/3x3_inst30perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_step/3x3_inst30perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_step/3x3_inst30perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/perturbed_step/3x3_inst30perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.8886986770755988, 0.16381677715556997, 0.3911952313182817], "cell_center": [1.8660254037844388, 6.147114317029974]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "cell_center": [1.8660254037844388, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst20_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 4: Place piece C with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/assembly/4x4_inst20assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "cell_center": [7.446152422706633, 6.0]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "cell_center": [2.4820508075688776, 6.0]}, {"index": 3, "angle": 30, "orig_width": 4, "orig_height": 1, "w": 3.964101615137755, "h": 2.8660254037844384, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523], "cell_center": [7.446152422706633, 2.0]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "cell_center": [2.4820508075688776, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n111\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst20_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x,y) = (0, 4).
<image_1>
Step 2: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).
<image_2>
Step 3: Place piece A with its upper-left corner at (x,y) = (1, 2).
<image_3>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [0, 2, 1, 4], "angle": 0, "flip": "none", "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "is_merged": true}, {"index": 2, "shape": [[0, 3, 0, 1], [2, 3, 1, 4]], "angle": 30, "flip": "none", "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "is_merged": false}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 0, "flip": "none", "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n1000\n1111\n1000\n\nPiece C:\n1111\n1000\n1000\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_for_valid_vis | [
"yes",
"no"
] |
|
4x4_inst75_var0_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst75/irregular_assembly/4x4_inst75invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 0, 2], "angle": 30, "flip": "none", "color": [0.9793998578171987, 0.9812459526092574, 0.9427181798334795], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 2, 4]], "angle": 60, "flip": "horizontal", "color": [0.9040775368572661, 0.57772211434449, 0.26938305630573245], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n01111\n11000\n11000\n11000\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
3x3_inst9_var4_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
Step 4: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).
<image_1>
Step 5: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst9/perturbed_part/3x3_inst9perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.1919730202293154, 0.3911833530705978, 0.8454502921977165]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.5904030260647292, 0.1502228379867938, 0.09526647902491858]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.5491620960992412, 0.8847398297155372, 0.43877106489933393]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.050666190966119684, 0.2152661154923936, 0.41855299588055594]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.505830367140229, 0.6887465524089847, 0.4889962320971758]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst3_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 2: Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).
<image_2>
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Place piece D with its upper-left corner at (x, y) = (1, 3).
<image_4>
Step 5: Place piece B with its upper-left corner at (x, y) = (1, 4).
<image_5>
Step 6: Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).
<image_6>
Step 7: Place piece E with its upper-left corner at (x, y) = (3, 3).
Step 8: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563]}, {"index": 6, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [2, 3, 2, 6], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813]}, {"index": 7, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369]}, {"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n1111\n\nPiece H:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst17_var1_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3).
<image_2>
Step 3: Place piece A with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst17/perturbed_step/3x3_inst17perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.5019930741412741, 0.012559332865545225, 0.17639361210978133], "cell_center": [1.5, 4.848076211353316]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.14133289160513685, 0.7931598690282321, 0.18641685245599515], "cell_center": [4.5, 4.848076211353316]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.3661900859965067, 0.7558139235341418, 0.8335971471271846], "cell_center": [1.5, 1.6160254037844386]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.5781587086361871, 0.8308911842343512, 0.6376093319739924], "cell_center": [4.5, 1.6160254037844386]}], "variant": "perturbed_step"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
4x4_inst6_var2_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).
Step 4: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 5: Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).
Step 6: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
<image_1>
Step 7: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst6/assembly/4x4_inst6assembly_step_7.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece G by about 90 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 3, 4], "color": [0.13437439136796736, 0.27065887983250636, 0.2175623391262027], "cell_center": [6.0, 10.0]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.5642191206300475, 0.5266511236435065, 0.01583621582154371], "cell_center": [2.0, 10.0]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.4742989639644474, 0.909668014873498, 0.8681758927696834], "cell_center": [2.0, 6.0]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.36824799770838956, 0.17303561687252822, 0.932534384866424], "cell_center": [10.0, 10.0]}, {"index": 6, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [3, 4, 0, 3], "color": [0.1635602218612643, 0.9092079607736911, 0.9337866032490502], "cell_center": [2.0, 2.0]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.5266413491581361, 0.1750305330495292, 0.268226050316132], "cell_center": [6.0, 6.0]}, {"index": 5, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 3, 4], "color": [0.04043697446808392, 0.08054772670054255, 0.40755271819790273], "cell_center": [10.0, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nPiece E:\n1\n\nPiece F:\n11\n\nPiece G:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst5_var3_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 3).
<image_1>
Step 2: Place piece A with its upper-left corner at (x,y) = (0, 1).
<image_2>
Step 3: Rotate piece G by about 30 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (2, 4).
<image_3>
Step 4: Place piece B with its upper-left corner at (x,y) = (1, 1).
<image_4>
Step 5: Rotate piece F by about 60 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (0, 4).
<image_5>
Step 6: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 1).
<image_6>
Step 7: Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/irregular_assembly/4x4_inst5irregular_assembly_step_7.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (1, 3).", "Place piece A with its upper-left corner at (x,y) = (0, 1).", "Rotate piece G by about 30 degrees clockwise. Place piece G with its upper-left corner at (x,y) = (2, 4).", "Place piece B with its upper-left corner at (x,y) = (1, 1).", "Rotate piece F by about 60 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 1).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 3, "shape": [0, 1, 0, 1], "angle": 30, "flip": "none", "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 2], "angle": 0, "flip": "none", "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437], "is_merged": false}, {"index": 6, "shape": [[3, 4, 0, 2], [1, 3, 0, 1]], "angle": 30, "flip": "none", "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175], "is_merged": false}, {"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333], "is_merged": false}, {"index": 5, "shape": [0, 1, 2, 4], "angle": 60, "flip": "none", "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846], "is_merged": true}, {"index": 2, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061], "is_merged": false}, {"index": 4, "shape": [0, 1, 1, 2], "angle": 60, "flip": "none", "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748], "is_merged": false}], "results": ["", "", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nPiece E:\n1\n\nPiece F:\n11\n10\n10\n\nPiece G:\n11\n10\n10\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst30_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).
<image_2>
Step 3: Place piece D with its upper-left corner at (x,y) = (0, 4).
Step 4: Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).
Step 5: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 1, 3], "angle": 90, "flip": "none", "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [0, 1, 0, 3]], "angle": 30, "flip": "none", "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "is_merged": false}, {"index": 3, "shape": [3, 4, 1, 4], "angle": 0, "flip": "none", "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "horizontal", "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1000\n1000\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n111\n\nPiece E:\n0001\n0001\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+partial_vis | [
"yes",
"no"
] |
|
4x4_inst7_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 5: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/perturbed_part/4x4_inst7perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.0038464181562460897, 0.5456025205471018, 0.8316288348193334]}, {"index": 4, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [2, 4, 1, 4], "color": [0.982403612127845, 0.027469345943991863, 0.7361933309757964]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.19476840970141396, 0.68707522398946, 0.14366332946109706]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.18526689525137774, 0.6222333081082303, 0.3116245006929087]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.5883107006707854, 0.8743059263428191, 0.51136848550568]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n\nPiece E:\n11\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst59_var3_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst59/irregular_assembly/3x3_inst59invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst59/irregular_assembly/3x3_inst59invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst59/irregular_assembly/3x3_inst59invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 0, "flip": "none", "color": [0.37038907806864063, 0.02669891258936674, 0.5729167093457774], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 2, 3]], "angle": 0, "flip": "horizontal", "color": [0.34642326513312416, 0.6825868668558092, 0.9916560425408335], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n010\n010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
3x3_inst72_var1_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst72/irregular_assembly/3x3_inst72invalid_irregular_assembly_step_2.png"], "instructions": ["", " Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "horizontal", "color": [0.8721773622006816, 0.41303145576010014, 0.7791921499016435], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 30, "flip": "none", "color": [0.5908631975774135, 0.17639180955650813, 0.08214364632741677], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst27_var0_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 3).
<image_1>
Step 2: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
<image_2>
Step 3: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/assembly/3x3_inst27assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/assembly/3x3_inst27assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/assembly/3x3_inst27assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/assembly/3x3_inst27assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973], "cell_center": [1.8660254037844386, 6.0]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.7341641971685425, 0.29244769077896215, 0.1293027898421113], "cell_center": [1.8660254037844386, 2.0]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_vis | [
"no",
"yes"
] |
|
4x4_inst20_var1_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
<image_1>
Step 4: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 4, "w": 4.464101615137754, "h": 3.7320508075688776, "label": "2x4", "piece": [0, 4, 0, 2], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n11\n\nPiece B:\n111\n111\n\nPiece C:\n111\n\nPiece D:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst11_var0_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_1>
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973], "cell_center": [6.897114317029974, 7.5]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822], "cell_center": [2.299038105676658, 7.5]}, {"index": 2, "angle": 90, "orig_width": 4, "orig_height": 2, "w": 2.0000000000000004, "h": 4.0, "label": "2x4", "piece": [2, 4, 0, 4], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693], "cell_center": [2.299038105676658, 2.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst10_var0_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).
<image_1>
Step 5: Place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst10/perturbed_part/3x3_inst10perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.08300347331815172, 0.9129260346492023, 0.030327958859172166]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 1, 3], "color": [0.6956976668525877, 0.5614724968196306, 0.20881351979388718]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.8361559109194318, 0.10012585524596118, 0.741018254845187]}, {"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.5852133457184661, 0.9478767577739693, 0.225765369032627]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3863759873563767, 0.3560346662754732, 0.9984770026551721]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n1\n1\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst27_var1_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.9816281227015189, 0.5664740351314982, 0.6376532394833729]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n11\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_intermediate_last_vis | [
"yes",
"no"
] |
|
4x4_inst12_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (3, 4).
Step 2: Place piece D with its upper-left corner at (x, y) = (0, 1).
Step 3: Place piece C with its upper-left corner at (x, y) = (0, 2).
<image_1>
Step 4: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst12/assembly/4x4_inst12assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/assembly/4x4_inst12assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/assembly/4x4_inst12assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/assembly/4x4_inst12assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/assembly/4x4_inst12assembly_step_4.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (3, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "valid": true, "config": [{"index": 1, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.6933282349034623, 0.28464064197742567, 0.5984440934517744], "cell_center": [7.5, 6.348076211353315]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.8799540670390662, 0.016815702542142485, 0.6851494150554925], "cell_center": [7.5, 2.1160254037844384]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.49483518787283254, 0.25660426038958584, 0.4007459306539174], "cell_center": [2.5, 2.1160254037844384]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.8269286759639897, 0.28853959708119414, 0.11506735623330777], "cell_center": [2.5, 6.348076211353315]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n111\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst17_var3_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece E with its upper-left corner at (x, y) = (2, 2).
<image_1>
Step 2: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
<image_3>
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
<image_4>
Step 5: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).
<image_5>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/perturbed_step/4x4_inst17perturbed_step_assembly_step_5.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (2, 2).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.09830256447954788, 0.3396191061459677, 0.9867290956314256], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9578521580074713, 0.8815921980787345, 0.19295089472973515], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3209357623770135, 0.4919116750200321, 0.05254088833875614], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.06114350981419958, 0.30119771230277814, 0.1293300317914955], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.8024254343287276, 0.5212933415712149, 0.6519422431117098], "cell_center": [5.598076211353316, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
4x4_inst38_var0_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Step 2: Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
Step 3: Flip piece C horizontally. Place piece C with its upper-left corner at (x,y) = (0, 4).
<image_1>
Step 4: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece C horizontally. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 3, "shape": [[2, 4, 1, 4], [0, 2, 2, 4]], "angle": 30, "flip": "none", "color": [0.12093478898180199, 0.6866466715293956, 0.13252558682790772], "is_merged": false}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.2834887826212631, 0.8656741309640128, 0.6531975744498982], "is_merged": false}, {"index": 2, "shape": [0, 2, 1, 2], "angle": 0, "flip": "horizontal", "color": [0.9282782748507362, 0.48858656271077405, 0.05954200460972181], "is_merged": true}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.16003991378313354, 0.02014673951971968, 0.3479685371859973], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1\n1\n\nPiece C:\n0111\n0111\n1100\n1100\n\nPiece D:\n111\n111\n011\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
4x4_inst13_var0_q+steps+all_for_valid_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece E with its upper-left corner at (x, y) = (0, 1).
<image_1>
Step 2: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).
<image_2>
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
<image_3>
Step 4: Place piece D with its upper-left corner at (x, y) = (2, 3).
<image_4>
Step 5: Place piece A with its upper-left corner at (x, y) = (0, 4).
<image_5>
Step 6: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
<image_6>
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/perturbed_part/4x4_inst13perturbed_part_assembly_step_6.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (2, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.7966424419178151, 0.9680914967906663, 0.866954291693426]}, {"index": 5, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.29384131363027277, 0.3163325797949277, 0.007829642754902055]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2805251122858946, 0.9715538225079458, 0.3810974789090861]}, {"index": 3, "angle": 0, "orig_width": 3, "orig_height": 3, "w": 3.0, "h": 3.0, "label": "3x3", "piece": [1, 4, 2, 5], "color": [0.13663939469484443, 0.7631849020052232, 0.6462586504062603]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [0, 1, 0, 2], "color": [0.08091420612656075, 0.9562651224873678, 0.23051757819828445]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 2, 4], "color": [0.9400983497113293, 0.32605090347507637, 0.5045925067978794]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n111\n111\n111\n\nPiece E:\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps+all_for_valid_vis | [
"no",
"yes"
] |
|
3x3_inst66_var0_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x,y) = (1, 2).
<image_1>
Step 2: Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst66/irregular_assembly/3x3_inst66invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (1, 2).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 1, 3], "angle": 0, "flip": "none", "color": [0.06174887048418565, 0.2337215698672812, 0.4202173017455749], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 30, "flip": "none", "color": [0.9339236099476395, 0.07222480453355551, 0.7957829886255944], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n010\n010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
|
3x3_inst46_var4_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_1>
Step 2: Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.3729218927568879, 0.31290847144958933, 0.3203892891755481], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 90, "flip": "horizontal", "color": [0.9286877744394081, 0.0842528242268854, 0.49084544991398305], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n100\n100\n111\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
4x4_inst4_var4_q+steps+all_intermediate_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x,y) = (2, 3).
<image_1>
Step 2: Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).
<image_2>
Step 3: Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 2).
<image_3>
Step 4: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).
<image_4>
Step 5: Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/irregular_assembly/4x4_inst4irregular_assembly_step_5.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (2, 3).", "Rotate piece E by about 60 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (2, 4).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.3298784267001694, 0.4254879586883913, 0.8323218982811694], "is_merged": false}, {"index": 4, "shape": [[0, 2, 0, 2], [0, 1, 2, 4]], "angle": 60, "flip": "none", "color": [0.9516920847941206, 0.09192754978443096, 0.034011632485778764], "is_merged": false}, {"index": 0, "shape": [2, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.1486163972137372, 0.09099753565850044, 0.9804276633019189], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 2], "angle": 30, "flip": "none", "color": [0.6633151367722326, 0.05563697103144172, 0.996308043298854], "is_merged": false}, {"index": 3, "shape": [3, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.7873704671604125, 0.6920579729169158, 0.06370548134717746], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n1100\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n\nPiece E:\n1100\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_intermediate_vis | [
"yes",
"no"
] |
|
4x4_inst55_var2_q+steps+partial_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst55/irregular_assembly/4x4_inst55invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 0, 3], "angle": 90, "flip": "none", "color": [0.48467087813086074, 0.8333251253686752, 0.226606070023177], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 3, 4]], "angle": 0, "flip": "vertical", "color": [0.9643179468173023, 0.2453124036567883, 0.8300162028796063], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n111\n\nPiece B:\n0010\n0010\n0010\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps+partial_vis | [
"no",
"yes"
] |
|
3x3_inst0_var3_q+steps+all_intermediate_last_vis | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).
<image_1>
Step 2: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst0/irregular_assembly/3x3_inst0irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "valid": true, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 30, "flip": "vertical", "color": [0.3256280422330665, 0.5203129240964942, 0.7395819324105462], "is_merged": true}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 30, "flip": "none", "color": [0.5107935611666639, 0.5856039458335469, 0.7112698396749424], "is_merged": false}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n011\n011\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps+all_intermediate_last_vis | [
"no",
"yes"
] |
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