once, which means it is easy to solve one part of the puzzle without disturbing what is already solved. In addition, each edge piece only has one possible orientation, meaning that if a given piece is in the correct position, it will always be orientated the correct way as well. Therefore, the solver never has to worry about changing the orientation of any pieces. Although not obvious at the first glance, the six-colour Dino Cube actually has two distinct configurations that represent a solved puzzle. The two solutions are mirror images of each other and the only visual difference between them is their colour schemes; for example, one solution has the colours Blue - Yellow - Red going clockwise around one vertex, while in the other these colours go anticlockwise. Mathematically, the puzzle is identical to Hoberman's BrainTwist, which is a tetrahedral puzzle that can "flip" inside out and reveal another set of four faces. Like the Dino Cube, The BrainTwist has twelve movable pieces, and each move rotates three pieces around one corner. It also likewise has two distinct solutions: one with the same colour on each of the faces and one with the same colour at each of the corners. Number of combinations The Dino Cube has twelve edge pieces. This means naturally there are twelve possible positions for the first given edge, however due to the lack of visible fixed "reference" pieces, all of these positions are rotationally symmetrical to each other. Therefore, the position of the first given edge is not taken into account. The remaining eleven edge pieces can be permutated in 11! different ways, relative to the first edge piece. Only even permutations of these pieces are possible (i.e. it is impossible to swap one pair of pieces while leaving the rest of the puzzle solved), which divides the limit by 2. The edge pieces cannot be flipped or misorientated (See Solving), therefore this is also not taken into account. The total number of possible combinations on the six-colour Dino Cube is therefore equal to: This number is low compared to the number of combinations of the Rubik's Cube (which has over 4.3×1019 combinations) but still larger than many other puzzles in the Rubik's Cube family, notably the Pocket Cube (over 3.6 million combinations) and the Pyraminx (just over 930 thousand combinations, excluding rotations of the trivial tips). Optimal solutions The number of possible