Problem

Source: 2020 CMO P4

Tags: combinatorics



Find the largest positive constant C such that the following is satisfied: Given n arcs (containing their endpoints) A1,A2,,An on the circumference of a circle, where among all sets of three arcs (Ai,Aj,Ak) (1i<j<kn), at least half of them has AiAjAk nonempty, then there exists l>Cn, such that we can choose l arcs among A1,A2,,An, whose intersection is nonempty.