CONO-SUR 1993 Problem 6

Prove that, given a positive integrer $n$ , there exists a positive integrer $k_n$ with the following property: Given any $k_n$ points in the space, $4$ by $4$ non-coplanar, and associated integrer numbers between $1$ and $n$ to each sharp edge that meets $2$ of this points, there's necessairly a triangle determined by $3$ of them, whose sharp edges have associated the same number.