Problem solving

Question

Eight friends are sitting around a circular table at Abby’s birthday party. Abby has only 3 party-poppers, so she wants to give them to three of her friends, so that two friends sitting next to each other both get a party-popper.

How many ways are there in which she can do this?

Answer 1

It can be done 8 ways.

First select one friend to get the first party popper. The friend to the left and right of that person shares it.

So the NEXT friend to get the next party popper sits TWO positions away from the first selection.

The third friend sits two positions away from the second selection.

Label the friends A-H.

If A gets the first party popper, then the other two are D, G

B " , then " " " are E, and H

C F and A

D G B

E H C

F A D

G B E

H C F