Sudoku and Algebra Completions
Whether a certain incomplete 9x9 grid of digits constitutes a valid Sudoku puzzle is a variant of the quasigroup completion problem. This article considers puzzles based on the completion problem for other classes of finite algebras. In particular, an incomplete collection of criteria for the appropriateness of candidate algebras are formalized using the language of first-order logic. Several classes of finite algebras are considered, including groups, quandles, semigroups, and Steiner systems.
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