INMO - 1992

Find the number of ways in which one can place the numbers \(1,2,3,...,{ n }^{ 2 }\) on the \({ n }^{ 2 }\) squares of \(n \times n\) chess board, one on each, such that the numbers in each row and each column are in arithmetic progression. (Assume n ≥ 3).

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