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 100% Solution by Steve Herman)

It would be interesting if we could also prove that it is not always possible to choose pairs such that no differences exceed 149.

Posted by Tristan on 2005-11-15 20:34:45