ar X iv : 1 20 1 . 07 49 v 1 [ cs . D S ] 1 J an 2 01 2 There is no 16 - Clue Sudoku : Solving the Sudoku Minimum Number of Clues Problem
نویسندگان
چکیده
We apply our new hitting set enumeration algorithm to solve the sudoku minimum number of clues problem, which is the following question: What is the smallest number of clues (givens) that a sudoku puzzle may have? It was conjectured that the answer is 17. We have performed an exhaustive search for a 16-clue sudoku puzzle, and we did not find one, thereby proving that the answer is indeed 17. This article describes our method and the actual search. The hitting set problem is computationally hard; it is one of Karp’s twenty-one classic NP-complete problems. We have designed a new algorithm that allows us to efficiently enumerate hitting sets of a suitable size. Hitting set problems have applications in many areas of science, such as bioinformatics and software testing. School of Mathematical Sciences, University College Dublin, Ireland. E-mail: [email protected]
منابع مشابه
There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration
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...
متن کاملThere is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem
We apply our new hitting set enumeration algorithm to solve the sudoku minimum number of clues problem, which is the following question: What is the smallest number of clues (givens) that a sudoku puzzle may have? It was conjectured that the answer is 17. We have performed an exhaustive search for a 16-clue sudoku puzzle, and we did not find one, thereby proving that the answer is indeed 17. Th...
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