Solving Sudoku Puzzles with Rewriting Rules

The aim of the sudoku puzzle (also known as number place in the United States) is to enter a numeral from 1 through 9 in each cell of a grid, most frequently a 9 × 9 grid made up of 3 × 3 subgrids, starting with various numerals given in some of the cells (the “givens”). Each row, column, and region must contain only one instance of each numeral. In this paper we show how a sudoku puzzle can be solved with rewriting rules using Maude. Three processes (scanning, marking up, and analysis) are the classical techniques for solving sudokus. Elimination is the main strategy that we have employed. The strategy what-if and several contingencies are also implemented.