A convex set $S$ on a plane, not lying on a line, is painted in $p$ colors. Prove that for every $n \ge 3$ there exist infinitely many congruent $n$-gons whose vertices are of the same color.
Source: Romania TST 1995 2.4
Tags: combinatorial geometry, combinatorics, Coloring, convex
A convex set $S$ on a plane, not lying on a line, is painted in $p$ colors. Prove that for every $n \ge 3$ there exist infinitely many congruent $n$-gons whose vertices are of the same color.