US-TST 2008 Problem 3

For a pair $A = (x_1, y_1)$ and $B = (x_2, y_2)$ of points on the coordinate plane, let $d(A,B) = |x_1 - x_2| + |y_1 - y_2|$ . We call a pair $(A,B)$ of (unordered) points harmonic if $1 < d(A,B) \leq 2$ . Determine the maximum number of harmonic pairs among 100 points in the plane.