Edmund's Brainteasers
Problem 16
Solution
Problem 16: The choir stalls. Solution
Suppose the girls sit on the organ side. Ann can sit in one of 3 positions (middle or one of the two ends). For each of these 3, Beth has a choice of the 2 remaining places, then Claire has to sit in the remaining place. There are therefore 6 ways the girls can sit on the organ side. Similarly there are 6 ways the boys can sit on the other side, and so 36 different arrangements with the girls on the organ side. There will also be 36 ways with the boys on the organ side making 72 ways in total. They can therefore have a different arrangement for 72 weeks, but on the 73rd they will have to reuse one of arrangements they have used before.