Sudoku Rectangle Completion (Extended Abstract)

Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled 9 × 9 square with numbers 1 through 9, subject to the constraint that each number must appear once in each row, each column, and each of the nine 3 × 3 blocks. Sudoku squares can be considered a subclass of the well-studied class of Latin squares. In this paper, we study natural extensions of a classical result on Latin square completion to Sudoku squares. Furthermore, we use the procedure developed in the proof to obtain asymptotic bounds on the number of Sudoku squares of order n.