MathDB
Double counting? KJMO 2024 antipode

Source: KJMO 2024 P2

November 9, 2024
inequalitiescombinatorics

Problem Statement

9999 different points P1,P2,...,P99P_1, P_2, ..., P_{99} are marked on circle OO. For each PiP_i, define nin_i as the number of marked points you encounter starting from PiP_i to its antipode, moving clockwise. Prove the following inequality.
n1+n2+⋯+n99≤99⋅982+49=4900n_1+n_2+\cdots+n_{99} \leq \frac{99\cdot 98}{2}+49=4900
Back to ProblemsView on AoPS