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A sequence of homothetic cubes

Source: MIPT Undergraduate Competition 2019 1.1 and 2.1

August 17, 2020
geometry3D geometrygeometric transformationhomothetytopology

Problem Statement

In R3\mathbb{R}^3, let there be a cube QQ and a sequence of other cubes, all of which are homothetic to QQ with coefficients of homothety that are each smaller than 11. Prove that if this sequence of homothetic cubes completely fills QQ, the sum of their coefficients of homothety is not less than 44.
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