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a surface of an n x n x n grid cube, covered by 1 x 2 rectangles

Source: 2012 Sharygin Geometry Olympiad Final Round 10.1

August 3, 2018
geometry3D geometrygridsquare gridcuberectangle

Problem Statement

Determine all integer nn such that a surface of an n×n×nn \times n \times n grid cube can be pasted in one layer by paper 1×21 \times 2 rectangles so that each rectangle has exactly five neighbors (by a line segment).
(A.Shapovalov)
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