Question 132
Find all integers $n$ such that we can color all the edges and the diagonals of a convex $n$-polygon by $n$ given colors satisfying the following conditions;
(1) Each of the edges or the diagonals is colored by only one color;
(2) For any three distinct colors, there exists a triangle whose vertices are vertices of the $n$-polygon and three edges are colored by these three colors.
(1) Each of the edges or the diagonals is colored by only one color;
(2) For any three distinct colors, there exists a triangle whose vertices are vertices of the $n$-polygon and three edges are colored by these three colors.