There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem
Abstract
The sudoku minimum number of clues problem is the following question: what is the smallest number of clues that a sudoku puzzle can have? For several years it had been conjectured that the answer is 17. We have performed an exhaustive computer search for 16-clue sudoku puzzles, and did not find any, thus proving that the answer is indeed 17. In this article we describe our method and the actual search. As a part of this project we developed a novel way for enumerating hitting sets. The hitting set problem is computationally hard; it is one of Karp's 21 classic NP-complete problems. A standard backtracking algorithm for finding hitting sets would not be fast enough to search for a 16-clue sudoku puzzle exhaustively, even at today's supercomputer speeds. To make an exhaustive search possible, we designed an algorithm that allowed us to efficiently enumerate hitting sets of a suitable size.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2012
- DOI:
- 10.48550/arXiv.1201.0749
- arXiv:
- arXiv:1201.0749
- Bibcode:
- 2012arXiv1201.0749M
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- 43 pages