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Rows in an Array

Source: ToT - 2001 Fall Junior A-Level #3

August 17, 2011
graph theorycombinatorics unsolvedcombinatorics

Problem Statement

Let n≥3n\ge3 be an integer. Each row in an (n−2)×n(n-2)\times n array consists of the numbers 1,2,...,nn in some order, and the numbers in each column are all different. Prove that this array can be expanded into an n×nn\times n array such that each row and each column consists of the numbers 1,2,...,nn.
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