MathDB
2019 All Russian MO Grade 11 P8

Source:

May 1, 2019

Problem Statement

A positive integer nn is given. A cube 3×3×33\times3\times3 is built from 2626 white and 11 black cubes 1×1×11\times1\times1 such that the black cube is in the center of 3×3×33\times3\times3-cube. A cube 3n×3n×3n3n\times 3n\times 3n is formed by n3n^3 such 3×3×33\times3\times3-cubes. What is the smallest number of white cubes which should be colored in red in such a way that every white cube will have at least one common vertex with a red one.
Thanks to the user Vlados021 for translating the problem.
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