C2

Part of 2015 JBMO Shortlist

Problems(1)

504 points on a unit disc, from any 5 points we can choose 2 with distance <=1

Source: JBMO Shortlist 2015 C2

2015

points are given in a plane such that from any five points we can choose two points with distance less than

1

unit. Prove that

504

of the given points lie on a unit disc.

combinatoricscombinatorial geometrypointsdistance