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 Monkey Dance 1 (Posted on 2004-03-19)
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?

 See The Solution Submitted by Sandeep Rating: 4.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: solution | Comment 24 of 30 |
(In reply to solution by Robin)

My list appears to be slightly incorrect. The 3-group solutions list should look like this:

2 3 16
2 4 15
2 5 14
2 6 13
2 7 12
2 8 11
2 9 10
3 4 14
3 5 13
3 6 12
3 7 11
3 8 10
4 5 12
4 6 11
4 7 10
4 8 9
5 6 10
5 7 9
6 7 8

The solution remains the same, though. I've also looked at the possibility of the dance never ending, but as each circle has exactly one arrow coming in and exactly one arrow coming out, the pidgeonhole primciple forces us into circles of arrows, so there's no way the dance can go forever.
 Posted by Robin on 2004-05-08 17:23:01

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