MathDB
Colored cube

Source: Iran TST 2002

September 28, 2006
3D geometrycombinatorics proposedcombinatorics

Problem Statement

A 10×10×1010\times10\times10 cube has 10001000 unit cubes. 500500 of them are coloured black and 500500 of them are coloured white. Show that there are at least 100100 unit squares, being the common face of a white and a black unit cube.
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