Minuet: A method to solve Sudoku puzzles by hand

TL;DR

The paper introduces the 'minuet' method, a systematic, human-solvable approach for solving all difficult 9x9 Sudoku puzzles efficiently, combining new markings and strategies.

Contribution

It presents a novel, comprehensive technique for humans to solve Sudoku puzzles systematically, unlike previous ad hoc tricks.

Findings

Successfully solved hundreds of 'evil' Sudoku puzzles.

Average solving time is just over 1 hour per puzzle.

The method can potentially solve all well-posed 9x9 Sudoku puzzles.

Abstract

This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and require too much memory. For humans, all one can find in the literature are individual tricks, which used together in ad hoc ways can be used to solve some puzzles--but not all. To the author's knowledge, a systematic procedure made up of well-defined steps that can be carried out by hand and solve all puzzles has not been devised. This paper proposes one such technique--the "minuet" method. It is based on a new system of markings and a new way of simplifying the puzzles that can be easily carried out by hand--or by computer. The author has solved hundreds of puzzles of the most difficult kind ("evil" in Sudoku's parlance) and never found one that could not be solved. The average time to solve one of these puzzles is slightly over 1 hour. It is conjectured that this method can solve all well-posed 9 x 9 puzzles. The method's distinguishing feature is a "minuet" strategy that is applied when the puzzle cannot be further simplified with basic tricks. The strategy consists in concurrently developing two potential solutions, sometimes alone and sometimes in concert as if they were dancing a minuet.