Solution: 2023-09 Permuted sums of reciprocals

Let \(\mathbb{S}_n\) be the set of all permutations of \([n]=\{1,\dots, n\}\). For positive real numbers \(d_1,\dots, d_n\), prove \[ \sum_{\sigma\in \mathbb{S}_n} \frac{1}{ d_{\sigma(1)}(d_{\sigma(1)}+d_{\sigma(2)}) \dots (d_{\sigma(1)}+\dots + d_{\sigma(n)}) } = \frac{1}{d_1\dots d_n}.\]

The best solution was submitted by 신민서 (KAIST 수리과학과 20학번, +4). Congratulations!

Here is the best solution of problem 2023-09.

Other solutions were submitted by 권도현 (KAIST 수리과학과 22학번, +3), 김명규 (KAIST 전산학부 19학번, +3), 김준홍 (KAIST 수리과학과 20학번, +3), 김찬우 (연세대학교 수학과 22학번, +3), 박기윤 (KAIST 새내기과정학부 23학번, +3), 박준성 (KAIST 수리과학과 석박통합과정 22학번, +3),이명규 (KAIST 전산학부 20학번, +3), 채지석 (KAIST 수리과학과 석박통합과정 21학번, +3), Anar Rzayev (KAIST 전산학부 19학번, +3). James Hamilton Clerk (+3), Matthew Seok (+3).

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