MathDB
TOT 039 1983 Spring S-01 S-A1 500 segments from 1000 concyclic points

Source:

August 18, 2019
combinatoricscombinatorial geometryDifferencenumber theory

Problem Statement

Numbers from 11 to 10001000 are arranged around a circle. Prove that it is possible to form 500500 non-intersecting line segments, each joining two such numbers, and so that in each case the difference between the numbers at each end (in absolute value) is not greater than 749749.
(AA Razborov, Moscow)