In the last decade the Sudoku puzzle has fixed itself in America’s puzzle consciousness. Sudoku puzzles share space with crossword puzzles and word finds in newspaper puzzle sections, and several books have been written for the Sudoku playing community. Mathematicians are among the most dedicated Sudoku players. Although some are content with simply solving puzzle after puzzle, others have used tools from combinatorics and algebra to study its important properties.
We investigate a variant of Sudoku called Cubic Sudoku, as well as Cubic Sudoku’s simpler relative, Cubic Shidoku. We successfully count the number of Cubic Shidoku puzzles in two different ways: by a direct argument and using Gröbner bases. We also make some observations about the difficulty of replicating these results for Cubic Sudoku.
Zoller, Nicholas, "The Mathematics of Cubic Sudoku" (2011). ACMS Conference Proceedings 2011. 26.
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