Christian writes of Mike Reid's nice example: << However, you are using the particularity that Dan allows to not analyze all the lines, if they are empty (why, Dan?).

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I agree with your implication that it's a more consistent condition if it's applied to *every* row or column, regardless of how many squares are filled initially. (I.e., it should apply to any row or column with k squares filled, 0 <= k <= N for an NxN square.) Your example is very nice too, Christian, especially considering that you posted it within about one minute of my question! << If we extend the Dan's condition to all the lines, empty or not, we can directly see that the last row (and the last column) cannot be filled.

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--Dan