Properties of Sudoku Puzzles.

Sudoku is a deceptively simple logic puzzle which has captured great public interest. Consisting of a 9×9 grid and further subdivided into ‘mini-grids’ of size 3×3, published puzzles are sufficiently simple in concept for wide sections of the population to attempt their solution, which still retaining a sufficient challenge for most through the necessity of applying several methods of reasoning. Academic interest in this class of puzzles has grown in recent years, due both to their relationship with other combinatorial structures (in particular Latin Squares) and their demonstrated connection to many real-world problems. This interest has taken the form of mathematical proof of specific puzzle properties and the application of search optimization techniques for its solution. In this paper, we highlight important features of the puzzle, and offer proof of several of them.