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You may have heard that last year it was proven that the smallest number of starting clues for a Sudoku game, guaranteeing a unique solution, is 17.
An example is shown below.

I am interested in the opposite:
What is the largest number of starting clues for a Sudoku game that does not guarantee a unique solution?

I have a lower bound of 63. This is if you take a solved Sudoku and delete every instance of two numbers (i.e., delete all the 1s and 2s). Alternatively, you could delete the top two rows, again yielding two different solutions for 63 starting clues.
Can you do better than 63, or is 63 is the highest?

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Tom
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  • It is a nice problem. (but your question will probably be closed down I'm afraid) – wildplasser Mar 28 '13 at 23:22
  • I also want to point out that I'm pretty sure that 17 thing was solved a long time ago. I remember doing a report on Sudoku in high school and that was already there. I think sudokus go way way back actually. But yes, I am curious about this question as well – Matt Dodge Mar 28 '13 at 23:24
  • 17 as a lower limit for givens was reported one, maybe two years ago. There you go : http://arxiv.org/abs/1201.0749 – wildplasser Mar 28 '13 at 23:26
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    Maybe this is a question for http://math.stackexchange.com/ – mikyra Mar 28 '13 at 23:29
  • Good question for math.stackexchange, but not this site. If this gets closed and you repost on math.SE, please link to the new question in the comments :) – BlueRaja - Danny Pflughoeft Mar 28 '13 at 23:32
  • [Here you go, x-posted to math.](http://math.stackexchange.com/questions/345244/maximum-number-of-clues-in-a-sudoku-game-that-does-not-produce-a-unique-solution) – Tom Mar 28 '13 at 23:40

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