Row-filled completion problem for sudoku
Abstract
Sudoku is a popular paper-pencil puzzle that involves completing a partially filled 9×9 Latin Square with the additional restriction that 3×3 sub-blocks (known as boxes or regions) must also have distinct entries. Completed sudoku puzzles are a special type of Latin Squares (that we term the Sudoku Latin Squares). We consider a type of completion problem in which the first j rows have been filled for some j < 9. We determine the values of j for which the completion is possible. Specifically, for the rowcompletion problem, we show that a completion is always possible for any j ≠ 5. We also present some results regarding the generalization of the problem to n2 × n2 size Sudoku Latin Squares. We also propose an analogue of Evans' conjecture for the Sudoku Latin Squares.
