Sudoku Rectangle Completion
arXiv:1704.08136
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 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 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 .