The numbers 1 to 200 are randomly assigned to points on the circumfrence of a circle. The points are divided into 100 pairs, with no point in two pairs. The two points in each pair are joined by a chord.
Is it always possible to choose 100 pairs so that no chords intersect and the difference between the values in any one pair does not exceed 150?
(In reply to
99% solution by Cory Taylor)
Excellent insight, Cory!
I don't see any holes in this.
I think that you have proved that at least one connection is always possible, because point between 51 and 150 will by this method be paired to a point that is noty between 51 and 150.
NICE WORK!
p.s. -- I think you just proved that the difference does not exceed 149.
Edited on November 5, 2018, 10:45 am
100% Solution
