AIME 2008b Problem 10

The diagram below shows a $4\times4$ rectangular array of points, each of which is $1$ unit away from its nearest neighbors. Define a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let $m$ be the maximum possible number of points in a growing path, and let $r$ be the number of growing paths consisting of exactly $m$ points. Find $mr$.