March 17, 2010

Minimum Hint Sudoku Hunt

The smallest number of hints that have been discovered in a Sudoku puzzle with a unique solution is 17. Nobody knows if there are any fully-determined Sudoku puzzles with 16 hints. Gordon Royle maintains a comprehensive list of the (currently) 49151 17-hint Sudoku puzzles that have been discovered. This list has grown over time, but nobody knows how incomplete this list might be.

The Sudoku Hint Machine now has two new features to help play with 17-hint puzzles:

  1. If you press the "Min Puzzle" button at the bottom, a random 17-hint puzzle (permuted and shuffled) from Gordon Royle's list will be chosen and shown (code here).
  2. If, while manually editing a puzzle, you arrive at a fully-constrained puzzle that is 17 hints or less, exclamation points will appear in a button at the bottom, and you can submit your puzzle to Gordon's list to see if it is a newly discovered minimum puzzle or not.

Note that an easy technique to discover other small-hint sudokus is to go into the hint machine with a 17-hint sudoku, solve a few extra squares, and then click on "Make Puzzle". The hint machine will subtract squares until the puzzle is minimal again, and it can often get back down to a different 17 squares.

If you find one that is 16 or fewer, definitely submit it to Gordon Royle's list. It will be the first one ever.

Posted by David at March 17, 2010 10:28 AM
Comments apparently there is a proof to show 16 or less are ambiguous.

Posted by: Roger at February 13, 2012 12:12 PM
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