The cells of a 5x5 square grid is numbered by the positive integers from 1 to 25 inclusively, with each number occurring in a cell exactly once.

Prove that there must exist two adjacent cells with common edge (not including diagonally) whose numbers have an absolute difference of at least 5.

In general with the numbers 1, 2,...., n² written on the cells of a nxn square grid in a random order such that each number occurs in a cell exactly once, will there always exist two adjacent cells with common edge (not including diagonally) whose numbers have an absolute difference of at least n, for every value of n ≥ 2?