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entire space can be partitioned into crosses made of 7 unit cubes

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p3

February 17, 2020
combinatorial geometrycombinatorics3D geometry

Problem Statement

Prove that the entire space can be partitioned into “crosses” made of seven unit cubes as shown in the picture. https://cdn.artofproblemsolving.com/attachments/2/b/77c4a4309170e8303af321daceccc4010da334.png