MathDB

Ten points are marked in the plane so that no three of them lie on a line. Each pair of points is connected with a segment. Each of these segments is painted with one of

k

colors, in such a way that for any

k

of the ten points, there are

k

segments each joining two of them and no two being painted with the same color. Determine all integers

k

1\leq k\leq 10

, for which this is possible.

Problem Statement