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How Many Faces Must be Painted?

Source: Spring 2006 Tournament of Towns Senior O-Level #5

September 9, 2015

Problem Statement

Pete has n3n^3 white cubes of the size 1×1×11\times1\times1. He wants to construct a n×n×nn\times n\times n cube with all its faces being completely white. Find the minimal number of the faces of small cubes that Basil must paint (in black colour) in order to prevent Pete from fulfilling his task. Consider the cases: a) n=3n = 3; (3 points) b) n=1000n = 1000. (3 points)
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