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sum of n from 1 to n^2 in a n x n board under conditions

Source: 1996 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

January 27, 2020
combinatoricsSumboard

Problem Statement

The cells of an n×nn \times n board are labelled with the numbers 11 through n2n^2 in the usual way. Let nn of these cells be selected, no two of which are in the same row or column. Find all possible values of the sum of their labels.
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