The director of a circus has decided to add a new performance, the monkey dance, to his show.

The monkey dance is danced simultaneously by 21 monkeys.
There are 21 circles drawn on the ground, and in the beginning, each monkey sits on a different circle.
There are 21 arrows drawn from circle to circle in such a way that exactly one arrow starts and exactly one arrow ends in each circle. No arrow can both begin and end at the same circle.

When the show begins, the monkeys dance in their circles until the ringmaster blows his whistle. At each whistle blow, the monkeys simultaneously jump from their circles to the next, following the arrows. The dance ends when all the monkeys have returned to the circles where they initially started.

The director wishes the dance to last as long as possible. What is the maximum number of whistle blows he can make before the dance ends?

(In reply to steve's solution by Steve Royer)

The trick is that you are not trying to maximize the product of the numbers, but their least common multiple. With groups of 3, 5, 6, and 7, the monkeys in the group of 3 will be 'home' every time the monkeys in the group of 6 are. Thus, that arrangement would really take only 5󬝳=210 whistles to complete.

Posted by DJ on 2004-03-24 11:51:08