MathDB

To each side of the regular

p

-gon of side length

1

there is attached a

1 \times 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?

Problem Statement