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 re(4): My solution by Charlie)

The obvious bug in my previous post is that it does not allow for the maximum just to be concentrated in one loop (one number).  The best you can do with 6 stations is to connect them all in a cycle of 6, not to have a cycle of 2 and a cycle of 4, devolving to just a period of 4.

Posted by Charlie on 2004-03-19 23:01:58