boxes or regions of a Sudoku. In some variants nonets are not equally shaped. Proper Sudoku – A Sudoku with one solution. Sudokus are always expected to be proper Sudokus unless the puzzle setter specifies otherwise. Region – Another term for the boxes of a Sudoku. In some variants regions are not equally shaped. Satisfactory puzzle – A puzzle that does not require trial and error (guessing). Note: the level of trial and error is usually not explicitly defined. Size – Refers to the size of a puzzle or grid, and can be described as a composite (i.e. 9×9), or the number of cells (i.e. 81). Symmetry – A Sudoku can have seven types of overall symmetry in its clue positions. They include: 90° rotational symmetry. 180° rotational symmetry. reflection symmetry on one orthogonal axis. reflection symmetry on two orthogonal axes. reflection symmetry on one diagonal axis. reflection symmetry on two diagonal axes. dihedral symmetry. In addition, groups of clues can display other types of symmetry, such as translational symmetry. Also refer to automorphic for a type of symmetry where the digits (not just their positions) play a role in another type of symmetry. Square – Another word for a cell of a Sudoku. In technical use the term is avoided because of ambiguity with boxes. Transformation – A manipulation of a Sudoku (or its grid) where it is changed or transformed into an essentially equivalent Sudoku. One example of a transformation is a permutation of the digits (such as changing all digits from "123456789" to "234567891"). There are five other Sudoku preserving transformations: row permutations within a band, column permutations within a stack, band permutations, stack permutations, and "reflection, transposition or rotation" (the later includes three transformations within a single class). A transformation can also be called a Sudoku preserving symmetry. See Mathematics of Sudoku for more details. Sudoku variants The classic 9×9 Sudoku format can be generalized to an N×N row-column grid partitioned into N regions, where each of the N rows, columns and regions have N cells and each of the N digits occur once in each row, column or region. This accommodates variants by region size and shape, e.g. 6-cell rectangular regions. (N×N Sudoku is square). For prime N, polyomino-shaped regions can be used and the requirement to use equal-sized regions, or have the regions entirely cover the grid can be relaxed. Other variations include additional