# Notice on POW 2020-21

POW 2020-21 is still open and anyone who first submits a correct solution will get the full credit.

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# Solution: 2020-22 Regular simplex

Let $$S$$ be the unit sphere in $$\mathbb{R}^n$$, centered at the origin, and $$P_1 P_2 \dots P_{n+1}$$ a regular simplex inscribed in $$S$$. Prove that for a point $$P$$ inside $$S$$,
$\sum_{i=1}^{n+1} (PP_i)^4$
depends only on the distance $$OP$$ (and $$n$$).

The best solution was submitted by 이준호 (수리과학과 2016학번, +4). Congratulations!

Here is his solution of problem 2020-22.

Other solutions was submitted by 고성훈 (수리과학과 2018학번, +3), 채지석 (수리과학과 2016학번, +3).

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