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Cheesboard!

Source: INMO 1992 Problem 7

October 4, 2005
combinatoricscountingChessboardArithmetic Progression

Problem Statement

Let n≥3n\geq 3 be an integer. Find the number of ways in which one can place the numbers 1,2,3,…,n21, 2, 3, \ldots, n^2 in the n2n^2 squares of a n×nn \times n chesboard, one on each, such that the numbers in each row and in each column are in arithmetic progression.
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