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46 squares are colored in red

Source: Indian National Maths Olympiad, Problem 4

February 5, 2006
geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

Some 46 squares are randomly chosen from a 9×99 \times 9 chess board and colored in red. Show that there exists a 2×22\times 2 block of 4 squares of which at least three are colored in red.
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