On the maximum number of isosceles right triangles in a finite point set

Let Q be a finite set of points in the plane. For any set P of points in the plane, SQ(P) denotes the number of similar copies of Q contained in P. For a fixed n, Erdýos and Purdy asked to determine the maximum possible value of SQ(P), denoted by SQ(n), over all sets P of n points in the plane. We consider this problem when Q = △ is the set of vertices of an isosceles right triangle. We give exact solutions when n ≤ 9, and provide new upper and lower bounds for S△(n).