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?

Maybe I am looking at this too naively. But, I think it is 20. I guess if I have to prove why. There are 21 circles. You blow the whistle once, the monkey goes to #2, blow it a second time it goes to #3. Showing a pattern of n - 1 = (number). 21-1=20. You would not count the first one as number 2, because then you would "spill over" and the dance would end. The dance would end at 21 whistles. So any more than 20 would be too many. The maximum times he could blow would be 20.

Posted by Jen on 2004-03-23 19:19:09