To each side of the regular p-gon of side length 1 there is attached a 1×k rectangle, partitioned into k unit cells, where k and p are given positive integers and p an odd prime. Let P be the resulting nonconvex star-like polygonal figure consisting of kp+1 regions (kp unit cells and the p-gon). Each region is to be colored in one of three colors, adjacent regions having different colors. Furthermore, it is required that the colored figure should not have a symmetry axis. In how many ways can this be done? geometryrectanglesymmetryColoringregular polygoncombinatorial geometrycombinatorics