Question 5
Ten points are marked in the plane so that no three of them lie on the same straight line. All points are connected with segments. Each of these segments is painted one of the $k$ colors.
For what positive integer $k$ ($1 \le k \le 5$) is it possible to paint the segments so that for any $k$ of the given 10 points there are $k$ segments with the ends at these $k$ points, all of these segments being painted $k$ different colors?
For what positive integer $k$ ($1 \le k \le 5$) is it possible to paint the segments so that for any $k$ of the given 10 points there are $k$ segments with the ends at these $k$ points, all of these segments being painted $k$ different colors?