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Square from cards

Source: St Petersburg Olympiad 2018, Grade 11, P2

June 21, 2018
combinatorics

Problem Statement

Vasya has 100100 cards of 33 colors, and there are not more than 5050 cards of same color. Prove that he can create 10×1010\times 10 square, such that every cards of same color have not common side.
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