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ASU 216 All Soviet Union MO 1975 coloring a kxkxk cube black and white

Source:

July 5, 2019

geometrycubeColoring

Problem Statement

For what

k

is it possible to construct a cube

k\times k\times k

of the black and white cubes

1\times 1\times 1

in such a way that every small cube has the same colour, that have exactly two his neighbours. (Two cubes are neighbours, if they have the common face.)

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