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painting unit cells in the plane

Source: Mongolia 1999 Grade 9 P1

May 4, 2021
geometrycombinatoricscombinatorial geometry

Problem Statement

The plane is divided into unit cells, and each of the cells is painted in one of two given colors. Find the minimum possible number of cells in a figure consisting of entire cells which contains each of the 1616 possible colored 2×22\times2 squares.