Let \(V\) be the set of tuples \((a_1,…,a_5)\) such that \(a_1 \leq a_2 \leq \cdots \leq a_5 \) belong to \(\mathbb{R}\) and satisfy \[ \sum_{1\leq i\leq 5} a_i >0, \quad \sum_{1\leq i<j \leq 5} a_i a_j >0, \quad \sum_{1\leq i<j< k \leq 5} a_ia_ja_k >0.\]

What is the maximum number \(p\) such that there exists a tuple \((a_1,…,a_5) \) in \(V\) whose \(a_p\leq 0 \)?

The best solution was submitted by 김준홍 (수리과학과 석박통합과정, +4). Congratulations!

Here is the best solution of problem 2026-03.

Other solutions were submitted by 김범석 (인하대, +3), 김은성 (서울대 수리과학과, +3), 김찬우 (연세대 수학과, +3), 신민규 (수리과학과 24학번, +3), 이상주 (경남대 수학교육과, +3), 장현준 (서울과학고 3학년, +3), 정서윤 (수리과학과 23학번, +3), 지은성 (수리과학과 석박통합과정, +3).