Denote \(P = \{(x, y, z) \in \mathbb{R^3}: 10< x,y,z <31\}\). Suppose a function \(f (v): \mathbb{R^3} \to \mathbb{R_{\geq 0}}\) satisfies:
(a) \(f(\lambda v) = \lambda^{25} f(v)\) for all \(v\in P\) and \(0<\lambda \in \mathbb{R}\),
(b) \(f(v+w) \geq f(v)\) for every \(v, w \in P\),
(c) \(f (v)\) is locally bounded.
Show that \(f (v)\) is locally Lipschitz in \(P\).

The best solution was submitted by 정영훈 (수리과학과 24학번, +4). Congratulations!

Here is the best solution of problem 2025-15.

Show that any set of d + 2 points in R^d can be partitioned into two sets whose convex hulls intersect.

The best solution was submitted by 정영훈 (수리과학과 24학번, +4). Congratulations!

Here is the best solution of problem 2025-14.

Other solutions were submitted by 김은성 (대구과학고, +3), 김지원 (전산학부 24학번, +3), 김찬우 (연세대 수학과, +3), 신민규 (수리과학과 24학번, +3), 이태민 (경남대 수학교육과, +3), 정서윤 (수리과학과 학사과정, +3), 지은성 (수리과학과 석박통합과정, +3).