Completed puzzles are always a type of Latin square. This means, each digit occurs exactly once in each row and once in each column. Sudoku rules also place more restrictions on the contents of individual regions: the same single integer may not appear twice
A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any of the 9 blocks of contiguous 3×3 cells. The relationship between the two theories is now completely known, after Denis Berthier proved in his book The Hidden Logic of Sudoku (May 2007) that a first-order formula that does not mention blocks (also called boxes or regions) is valid for Sudoku if and only if it is valid for Latin Squares (this property is trivially true for the axioms and it can be extended to any formula). (Citation taken from p. 76 of the first edition: "any block-free resolution rule is already valid in the theory of Latin Squares extended to candidates" – which is restated more explicitly in the second edition, p. 86, as: "a block-free formula is valid for Sudoku if and only if it is valid for Latin Squares").
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