# Solution: 2012-23 A solution

Prove that for each positive integer $$n$$, there exist $$n$$ real numbers $$x_1,x_2,\ldots,x_n$$ such that $\sum_{j=1}^n \frac{x_j}{1-4(i-j)^2}=1 \text{ for all }i=1,2,\ldots,n$ and $\sum_{j=1}^n x_j=\binom{n+1}{2}.$

The best solution was submitted by Taehyun Eom (엄태현), 2012학번. Congratulations!

Here is his Solution of Problem 2012-23.

Alternative solutions were submitted by 박민재 (2011학번, +3, Solution), 김태호 (수리과학과 2011학번, +2), 이명재 (2012학번, +2).

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