Problem

Source: Moldova NMO 2002 grade 10 problem nr.4

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In each line and column of a table $ (2n + 1)\times (2n + 1)$ are written arbitrarly the numbers $ 1,2,...,2n + 1$. It was constated that the repartition of the numbers is symmetric to the main diagonal of this table. Prove that all the numbers on the main diagonal are distinct.