Let \(P_1,P_2,\ldots,P_n\) be n points in {(x,y): 0<x<1, 0<y<1} (n>1). Let \(r_i=\min_{j\neq i} d(P_i,P_j)\) where d(x,y) means the distance between two points x and y. Prove that \(r_1^2+r_2^2+\cdots+r_n^2\le 4\).

The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2009-13.