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

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

Here is his Solution of Problem 2009-13.

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