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Jan 10, 2012 · There is no 16-clue Sudoku, mathematician shows. As all Sudoku enthusiasts know, a proper Sudoku puzzle must have only one correct answer. But until now, it has been mere conjecture that the minimum number of clues needed to complete the puzzle, with only one unique solution, is 17, and puzzles with 16 clues or fewer must have multiple solutions.
Jan 6, 2012 · Now a year-long calculation proves there are no 16-clue puzzles. By. Emerging Technology from the arXiv. January 6, 2012. Sudoku is a number puzzle consisting of a 9 x 9 grid in which...
- Sudoku Minimum Number of Clues Problem
- Sudokus with 17 Clues Or More May Have Multiple Solutions
- Sudoku Variants Are A Different Story
But it’s not just puzzles with 7 or fewer clues that can have multiple solutions. Finding the minimum number of clues required in order for a Sudoku to have a unique solution is known as the Sudoku minimum number of clues problem. The answer to this problem is 17. While a concrete mathematical proof has not been found, mathematicians have analyzed ...
Just because the minimum number of clues required for a Sudoku puzzle to have one unique valid solution is 17, it doesn’t mean that Sudoku with 17 or more clues can only have one unique solution. It’s possible for these puzzles to have multiple solutions, again based on how the clues are given. For example, if every 1, 2, and 3 digits in a grid was...
Everything we’ve talked about so far only relates to regular Sudoku puzzles and not any variants with additional constraints. Variants like Thermo Sudoku where there are different types of clues or Chess Sudokuwhere there are different types of constraints complicate matters significantly. But again, whether there is a unique solution or multiple v...
Jan 6, 2012 · Gary McGuire of University College Dublin shows in a proof posted online on 1 January 1 that the minimum number of clues — or starting digits — needed to complete a puzzle is 17; puzzles with...
- Eugenie Samuel Reich
- 2012
We apply our new hitting set enumeration algorithm to solve the sudoku mini-mum 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.
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.
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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.
