Problem number four. Maya has four differently colored pens. She wants to color the three-striped rectangular flag shown in the diagram to the right so that each stripe is a single color and no two adjacent stripes are the same color. In how many ways can she do this? There are four ways to color the top stripe. So that's going to give us four ways of the first, right? And now we have to look at the second stripe. There are three ways to color the middle stripe since it cannot be the same color as the top stripe and thus we only have three choices for what color to use. Now the bottom stripe, we still once again only have three choices because it can't be the same color as the middle stripe. Notice that it can be the same color as the top stripe, we just have to worry about it being the same color as the middle stripe. Thus in total there's four times three times three or 36 total ways to color the flag and thus our answer is choice D.

flag coloring

adjacent stripes

color choices

combinatorics

problem solving