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(3n + 1) * (3n + 1) table

Source: China TST 1992, problem 5

June 27, 2005
geometrygeometric transformationrotationinductionrectanglecombinatorics unsolvedcombinatorics

Problem Statement

A (3n+1)×(3n+1)(3n + 1) \times (3n + 1) table (n∈N)(n \in \mathbb{N}) is given. Prove that deleting any one of its squares yields a shape cuttable into pieces of the following form and its rotations: ''L" shape formed by cutting one square from a 2×22 \times 2 squares.
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