MathDB

Let

n\ge 2

be a positive integer. Fill up a

n\times n

table with the numbers

1,2,...,n^2

exactly once each. Two cells are termed adjacent if they have a common edge. It is known that for any two adjacent cells, the numbers they contain differ by at most

n

. Show that there exist a

2\times 2

square of adjacent cells such that the diagonally opposite pairs sum to the same number.

Problem Statement