Purple Comet 2009 HS Problem 6
Source:
April 21, 2012
Problem Statement
Wiles county contains eight townships as shown on the map. If there are four colors available, in how many ways can the the map be colored so that each township is colored with one color and no two townships that share a border are colored with the same color?[asy]
path[] P=
{
(0,0)--(13,0)--(13,11)--(0,11)--cycle,
(5,0)--(13,6)--(13,0)--cycle,
(13,7)--(13,11)--(7,11)--cycle,
(0,0)--(7,0)--(7,11)--(0,11)--cycle,
(0,5)--(0,11)--(11,11)--cycle,
circle((4,7),2.5),
(0,0)--(5,0)--(2,11)--(0,11)--cycle,
(0,5)--(0,11)--(5,11)--cycle,
};
for(int k=0;k