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Points in frames

Source: Iranian Our MO 2020 P7

March 12, 2020
combinatorics

Problem Statement

75017501 points in a 96×9696 \times 96 square is marked. We call the 4×44 \times 4 square without its central 2×22 \times 2 square a frame. Prove that there exist a frame with sides parallel to the 96×9696 \times 96 square (not necessarily from the grid lines) that contains at least 1010 marked points.
Proposed by Negar Babashah, Shima Amirbeygie Rated 5
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