Determine the maximal number of disjoint crosses (5 squares) which can be put inside chessboard such that sides of a cross are parallel to sides of the chessboard.
Saudi Arabian Mathematical Competitions
Solution
Let's note, that 4 corner cells can't be covered by crosses. So we assume that they are removed from the board and we have only 60 cells.
From the first row at most two cells can be covered by crosses. So at least 4 cells will be not covered. The same argument works for last row, first column and last column. So at most cell can be covered, which means at most 8 crosses can be used. It remains to show the example with 8 crosses.
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