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 re: Solution? Spoiler? by Charlie)

Hmm.  Yes.  Thanks, Charlie.  My observation 1 is wrong, so my argument is also.  No wonder you couldn't follow it!!

Back to the drawing board.

I have some faint hope that maybe my construction will still be a counterexample, but I clearly have more work to do.

Posted by Steve Herman on 2005-11-12 12:09:31