CN-TST 2014 Problem 6

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.