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Faces of a cube $9\times 9\times 9$

Source: All-Russian 2007

May 4, 2007
geometry3D geometrycombinatorics proposedcombinatorics

Problem Statement

Faces of a cube 9×9×99\times 9\times 9 are partitioned onto unit squares. The surface of a cube is pasted over by 243243 strips 2×12\times 1 without overlapping. Prove that the number of bent strips is odd. A. Poliansky
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