Question 29. Emma is playing with the seven caterpillar puzzle pieces shown. She wants to build a caterpillar that has one head, one tail, and one, two, or three puzzle pieces in between. How many different caterpillars can Emma build? First let's look at the head pieces. We can choose one of the two head pieces for the caterpillar, giving us two options. Now let's look at the middle pieces. Notice how both the tail pieces have a rectangular connection, and how the cherry piece is the only middle piece that ends in a rectangular connection. This means that we need the cherry piece to be at the end of the middle section. From there, since we can have anywhere from one to three middle pieces, we can add or not add the apple and grape pieces in any order in front of the cherry piece. This gives us five different possibilities for the middle section. Cherry, apple cherry, grape cherry, apple grape cherry, and grape apple cherry. Now let's look at the tail pieces. We can choose one of the two tail pieces for the caterpillar, giving us two options. Multiplying the number of options we have for all three sections of the caterpillar together gives us a total of 20 different caterpillars.

caterpillars

puzzle pieces

combinations

head choices

tail choices