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Find 3x3 square without its central cell in 72x72 square

Source: IV Caucasus Mathematic Olympiad

April 7, 2019
combinatorics

Problem Statement

Vova has a square grid 72×7272\times 72. Unfortunately, nn cells are stained with coffee. Determine if Vova always can cut out a clean square 3×33\times 3 without its central cell, if a) n=699n=699; b) n=750n=750.
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