A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles

T he puzzle Sudoku has become the passion of many people the world over in the past few years. The interesting fact about Sudoku is that it is a trivial puzzle to solve. The reason it is trivial to solve is that an algorithm exists for Sudoku solutions. The algorithm is a tree-based search algorithm based on backtracking in a tree until a solution is found. If all a person needs to do is sit down at their personal computer, punch in the numbers given in the puzzle, and then watch a computer program compute the solution, we can reasonably ask why a person would bother to struggle to solve Sudoku puzzles. The reason is that people enjoy struggling with pencil and paper to work out Sudoku solutions. Herzberg and Murty (2007, p. 716) give two reasons for the enjoyment of this struggle: First, it is sufficiently difficult to pose a serious mental challenge for anyone attempting to do the puzzle. Secondly, simply by scanning rows and columns, it is easy to enter the “missing colors”, and this gives the solver some encouragement to persist. This paper develops an algorithm for solving any Sudoku puzzle by pencil and paper, especially the ones classified as diabolical.