1988 AJHSME Problems/Problem 16
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Problem
Placing no more than one in each small square, what is the greatest number of 's that can be put on the grid shown without getting three 's in a row vertically, horizontally, or diagonally?
Solution
By the Pigeonhole Principle, if there are at least 's, then there will be some row with 's. We can put in by leaving out the three boxes in one of the main diagonals.