MathDB

Mark

4 \cdot k

points in a circle and number them arbitrarily with numbers from

1

4 \cdot k

. The chords cannot share common endpoints, also, the endpoints of these chords should be among the

4 \cdot k

points.
i. Prove that

2 \cdot k

pairwisely non-intersecting chords can be drawn for each of whom its endpoints differ in at most

3 \cdot k - 1

. ii. Prove that the

3 \cdot k - 1

cannot be improved.

Problem Statement