Sudoku Variations

Although the 9x9 grid with 3x3 regions is by far the most common, numerous variations abound: sample puzzles can be 4x4 grids with 2x2 regions; 5x5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has previously featured a 6x6 grid with 2x3 regions and a 7x7 grid with six heptomino regions and a disjoint region. Even the 9x9 grid is not always standard, with Ebb regularly publishing some of those with nonomino regions. Larger grids are also possible, with Dell regularly publishing 16x16-grid Number Place Challenger puzzles and Nikoli proffering 25x25 Sudoku the Giant behemoths. Another common variant is for the numbers in the main diagonals of the grid to also be required to be unique; all Dell Number Place Challenger puzzles are of this variant.

There is an obvious similarity to these puzzles and Latin squares, the solved grids necessarily being Latin squares with the additional regional restriction - hence one of its published names, Quadrum Quandary, being rather punny ('quadrum' is Latin for 'square'). Although the quantity of Latin squares for many given sizes is known, including 9x9, the number of valid Sudoku solution grids for even the standard 9x9 grid with 3x3 regions is apparently unknown; members of the Dell forum are presently working on the problem.