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Balanced table containing the numbers 1,2,...,n^2

Source: Moldova IMO-BMO TST 2003, day 3, problem 4

August 16, 2008

Problem Statement

A square-table of dimensions n×n n\times n, where n∈N∗ n\in N^*, is filled arbitrarly with the numbers 1,2,...,n2 1,2,...,n^2 such that every number appears on the table exactly one time. From each row of the table is chosen the least number and then denote by x x the biggest number from the numbers chosen. From each column of the table is chosen the least number and then denote by y y the biggest number from the numbers chosen. The table is called balanced iff x \equal{} y. How many balanced tables we can obtain?
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