MathDB
Table with cells

Source: All Russian Olympiad 2017,Day2,grade 9,P8

May 3, 2017
combinatorics

Problem Statement

Every cell of 100×100100\times 100 table is colored black or white. Every cell on table border is black. It is known, that in every 2×22\times 2 square there are cells of two colors. Prove, that exist 2×22\times 2 square that is colored in chess order.
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