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Swiss crosses insides a 7x7 square, divided into unit squares

Source: Switzerland - Swiss TST 2002 p4

February 18, 2020
combinatorial geometrycombinatorics

Problem Statement

A 7×77 \times 7 square is divided into unit squares by lines parallel to its sides. Some Swiss crosses (obtained by removing corner unit squares from a square of side 33) are to be put on the large square, with the edges along division lines. Find the smallest number of unit squares that need to be marked in such a way that every cross covers at least one marked square.