Let \(g(t): [0,+\infty) \to [0,+\infty)\) be a decreasing continuous function. Assume \(g(0)=1\), and for every \(s, t \geq 0 \) \[t^{11}g(s+t) \leq 2024 \; [g(s)]^2.\] Show that \(g(11) = g(12)\).

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

Here is the best solution of problem 2024-19.

Other solutions were submitted by 김찬우 (연세대학교 수학과 22학번, +3), 양준혁 (KAIST 수리과학과 20학번, +3), 이명규 (KAIST 전산학부 20학번, +3).