2

Part of 1996 Bundeswettbewerb Mathematik

Problems(1)

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

The cells of an

n \times n

board are labelled with the numbers

1

n^2

in the usual way. Let

n

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.

combinatoricsSumboard