MathDB

Consider an

n \times n

array of numbers

a_{ij}

(standard notation). Suppose each row consists of the

n

numbers

1,2,\ldots n

in some order and

a_{ij} = a_{ji}

for

i , j = 1,2, \ldots n

. If

n

is odd, prove that the numbers

a_{11}, a_{22} , \ldots a_{nn}

are

1,2,3, \ldots n

in some order.

Problem Statement