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# Sudoku Mystery Solved

By siliconindia   |   Monday, 09 January 2012, 10:06 Hrs
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Bangalore: Good news for all Sudoku fans. Sudoku will be a lot easier with the game giving you 17 clues now. As per a recent research conducted by Gary McGuire and his team at University College, Dublin, it was noted that a Sudoku puzzle must provide at least 17 clues or starting numbers, in order to be valid as any fewer will not produce a unique answer, as reported by ANI. It was noted that there must be some minimum number of clues required for a valid puzzle.

The Mathematicians have proved that it is not possible to create a 16-clue puzzle with a unique answer, so the minimum number of clues must be 17. If a starting 9x9 grid has just a single "1" filled in, then it is clear that this could correspond with many different answers, though; no one knew the exact number of clues required.

Sudoku enthusiasts had found nearly 50,000 17-clue puzzles, but no one had managed to find a completely unique 16-clue puzzle. The closest anyone got was a 16-clue puzzle with just two possible solutions. In order to solve the problem, McGuire and his team used a piece of software that could check any completed Sudoku grid for the presence of n-clue puzzles buried within it. The earlier version of their software took an hour to search a single completed grid, but the latest revision can check for 16-clue puzzles in just a few seconds.

After a research by the team which took them quite a few years it was discovered that there was no 16-clue puzzles, which also implies there are no 15 or fewer clue puzzles either, so the minimum must be 17.

Apart from solving the Sudoku mystery the team said that their work could also be applied to solving the vertex cover problem that arises in the branch of mathematics known as graph theory and has applications in gene sequencing and software testing.