# Show there is always a pair at least 16 apart

The integers 1 to 4 are positioned in a 6 by 6 square grid as shown and cannot be moved. The integers 5 to 36 are now placed in the 32 empty squares. Prove that no matter how this is done, the integers in some pair of adjacent squares (i.e. squares sharing an edge) must differ by at least 16.

$$\begin{array}{|l|l|l|l|l|l|} \hline & & & & & \\ \hline & 1 & & & 2 & \\ \hline & & & & & \\ \hline & & & & & \\ \hline & 3 & & & 4 & \\ \hline & & & & & \\ \hline \end{array}$$