Question 141
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 $1 \lt d(A, B) \le 2$. Determine the maximum number of harmonic pairs among 100 points on the plane.
(This problem was suggested by Zuming Feng and Oleg Golberg.)
(This problem was suggested by Zuming Feng and Oleg Golberg.)