Juku paints exactly 30 unit squares of a table black. After that, Miku covers up exactly 4 rows and 4 columns. Can Juku ensure by the choice of the squares to be coloured that at least 10 black unit squares are left uncovered?
Estonia — Open Contests
Solution
Juku can paint 30 unit squares in such a way that each row contains exactly 3 black unit squares and each column contains exactly 2 of them (Fig. 1). When Miku chooses 4 rows and 4 columns, they contain at most black unit squares altogether. Hence at least 10 black unit squares remain uncovered.
Fig. 1
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