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54 squares to cover 3x3x3 - All-Russian MO 1999 Regional (R4) 8.8

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September 25, 2024
combinatoricscombinatorial geometry3D geometrygeometry

Problem Statement

An open chain was made from 5454 identical single cardboard squares, connecting them hingedly at the vertices. Any square (except for the extreme ones) is connected to its neighbors by two opposite vertices. Is it possible to completely cover a 3×3×33\times 3 \times3 surface with this chain of squares?