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N point on a circle

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005

combinatorics proposedcombinatorics

Problem Statement

Let

n

points be given on a circle, and let

nk + 1

chords between these points be drawn, where

2k+1 < n

. Show that it is possible to select

k+1

of the chords so that no two of them intersect.