How to determine correctness.

Everything about Sudoku that doesn't fit in one of the other sections

How to determine correctness.

Postby kratos » Mon Apr 11, 2005 11:31 am

My wife and I solve Sodukos (usually). Occasionally one of us will turn to the other and say, "I think I've done it, will you check it for me?"

Is it possible to check a Sudoku puzzle without checking every box, row and column, by, say, checking three rows and then three columns, and if they check out OK the rest of the puzzle must be right.

What is the least checking one can do to be certain the puzzle has been solved?
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Joined: 29 March 2005

Postby Guest » Thu Apr 14, 2005 12:03 am

I used to think that you need to check everything (i.e. all rows, cols & boxes), but just realised this is not true - just very nearly true.

The least wrong a solution can be is for 1 cell to have the wrong digit. This would mean that 3 units (1 row, 1 col and 1 box) are incorrect. So, you can get away with only testing 25 of the 27 units.

I don't think it matters which 25 you chose - but it would probably take longer to decide than to check the last 2! You'd also need to be more careful as you have potentially reduced your chances of finding the error by 2/3. All in all, not very useful!

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