Question 27
(BLR) Ten points such that no three of them lie on a line are marked in the plane. 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 with no two being painted the same color. Determine all integers $k$, $1\le k\le10$, for which this is possible.