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?
must the points be in consecutive order, ie. must 2 fall between 1 and 3 on the circumference, etc?
otherwise producing non-intersecting chords and pairs whose differences are < 150 are independent problems.
are they consecutive?
