A sudoku must have at least 17 clues in the beginning in order to be resolved

The mathematician at the University of Dublin, Gary McGuire, has used a complex algorithm and “millions of hours of supercomputing time” to determine that a sudoku cannot be completed unless it has a minimum of 17 clues in the beginning, since puzzles with 16 or fewer clues “do not have a unique solution”.

This game, which became popular in Japan and is now a common hobby all over the world, usually starts with 25 clues, as the scientist duly noted. The fewer clues it has, the more difficult is its resolution.

The complexity of sudoku has led it to be studied by mathematicians. Now, McGuire has come to this conclusion after working for two years on the complex algorithm that has brought about the solution. He spent about seven million CPU hours searching through possible grids. “The only realistic way to do it was the brute force approach,” noted McGuire, who added that his research has inspired him “to push computing and mathematical techniques to the limit”.

McGuire has simplified the work of some of his companions, who preceded him in this research, by designing an algorithm to prevent what the scientist called “unavoidable sets” which could lead to “multiple solutions”.

As stated by the journal “Nature”, the announcement of this finding occurred in a mathematical congress held in Boston (USA) on January 7th where he received the approval of his peers. “The approach is reasonable and it’s plausible,” says Jason Rosenhouse, a mathematician at James Madison University (USA).