POINTS AND COLOR LINES

There are X points on a plain paper such that no three of them are collinear. Using four different colors, you will draw lines connecting each point with every other point.

Conditions:

-No triangle formed by these connections (and having these points as corners) would be monochromic.
-At no point can all four colors be found.

What is the maximum possible value for X?

Popularity: 41.7 %     Difficulty: 86.5 %