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Johan

Joined: 22/12/2006 20:08:51
Messages: 945
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Prove or disprove the following:
In a 9x9 Sudoku-square one randomly places the numbers 1...8. There is at least one field such that if any of the numbers 1...9 is placed there, the Sudoku-square can be filled in to a (not necessarily unique) complete solution.

(source: Matthijs Coster in NieuwArchief #2, 2006)

Let's answer in white text to avoid spoilers.
Maarten

Joined: 22/12/2006 20:10:10
Messages: 615
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I'm not sure I understand the question. Could you clarify it?
achan1058

Joined: 19/04/2008 05:22:28
Messages: 16
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If you mean by placing 1 of each 1,2,3,4,5,6,7,8 on a 9x9 square, then asking whether there is a box which we put any of 1,...,9 and complete it in a sudoku fashion, then it is pretty easy to disprove. The solution is

Put 123 on the first row, 456 on the second row, both in the top left box. Put 78 on the third row, top middle box. Now you cannot satisfy it no matter what, without even caring about the 1,...9.
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