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21 pieces, bw, on the squares of a 3x7 rectangle

Source: Spanish Mathematical Olympiad 1994 P5

July 31, 2018
combinatoricsgridgeometryrectangle

Problem Statement

Let 2121 pieces, some white and some black, be placed on the squares of a 3×73\times 7 rectangle. Prove that there always exist four pieces of the same color standing at the vertices of a rectangle.