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Monkey Dance 1 (Posted on 2004-03-19) Difficulty: 3 of 5
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.)
Solution re: My solution | Comment 3 of 30 |
(In reply to My solution by Iain)

I disagree that all the numbers of the Loop Sizes have to be prime.

What we are dealing with is a situation where you need to find a set of whole numbers (that cannot include 1) whose sum is 21 and whose Least Common Multiple is maxmized.

A solution I found is 2, 3, 4, 5, and 7.  The least common multiple is 2^2 * 3 * 5 * 7 = 420.

I don't know if that is the maximum solution, but I'm sure Charlie will provide an exhaustive proof of the maximum =)


  Posted by nikki on 2004-03-19 14:43:49
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