Biggest Sudoku puzzle solved

How many positions in the Sudoku board must be filled from the beginning in order for the game to have a unique solution? The question has puzzled mathematicians for years. But now an Irish researcher claims to have solved the riddle by having a supercomputer run a special algorithm for days: the answer he found is 17.

Sudoku

In the Sudoku puzzle, which became famous first in Japan and later around the world, the player is asked to fill in a 9-by-9 table with numbers from 1 to 9. But the table must be filled in such a way that no number is repeated in the same row, column, or 3 by 3 sub-matrix.

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In order for the game to start, certain positions on the board must be filled in advance. And the more filled positions, the easier the game becomes. Newspaper-published Sudoku puzzles usually give about 25 known numbers.

Because no one had ever succeeded in devising a game with 16 known numbers that had a single solution, mathematicians had conjectured that the minimum possible number of filled positions in the table is 17. One way to confirm this guessing is to solve all possible games with 16 filled positions. But that would take forever.

The solution

Gary McGuire of University College Dublin simplified the problem by first identifying the arrangements of numbers on the completed table which can be interchanged and thus lead to multiple solutions.

In the next phase, McGuire had to show that there is no puzzle of the 16 known positions that can rule out all of the above arrangements. It took days of calculations at a supercomputing center in Dublin, but finally the mathematician proved the old conjecture.

Or so he claims, since his fellow mathematicians will take months or even years to confirm or disprove him.

However, as the Nature website reports, mathematicians who were informed of McGuire's solution at a conference held in Boston on January 7th suspect that the solution is correct and represents a major advance in the mathematics of Sudoku.