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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