MathDB
TOT 026 1982 Autumn J4 20 points in circle, 20 equal arcs, 10 chords

Source:

August 18, 2019
geometrycombinatorial geometrypointscirclesarcchord

Problem Statement

(a) 1010 points dividing a circle into 1010 equal arcs are connected in pairs by 55 chords. Is it necessary that two of these chords are of equal length?
(b) 2020 points dividing a circle into 2020 equal arcs are connected in pairs by 1010 chords. Prove that among these 1010 chords there are two chords of equal length.
(VV Proizvolov, Moscow)