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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(3): My solution | Comment 5 of 30 |
(In reply to re(2): My solution by Charlie)

The sensible way to think through this is to realize that you gain nothing from having duplicates of a number. So, listing off the first few primes is a good idea. 2 3 5 7. You have 4 left, which can be added on to one of the numbers, or left alone. If you add it on to one of the numbers, you will get 4 times the other numbers to add on. However, if you leave it alone, you will get double all the numbers. Adding 4 to 2 doesn't change anything, and adding 4 to 7 gives a useless 7. So adding 5 to 5 or 7 to 7 is better than 4 to 5 or 5 to 7, and thus, adding 4 as another number is best.
 Posted by Gamer on 2004-03-19 16:57:13

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