Question 112
The sides and diagonals of a regular $n$-gon are colored in $k \ge 3$ colors. For each color $i$, between every two vertices of the polygon there exists a path consisting only of segments of color $i$. Prove that there exist three vertices of the polygon $A$, $B$, and $C$ such that the line segments $AB$, $BC$, and $AC$ are multicolor.
(Emil Kolev)
(Emil Kolev)