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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)

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 My solution | Comment 2 of 30 |

Since one arrow starts and ends in each circle, the individual circles must be connected together in larger circles of the arrows.

To create the largest number of whistle blows, the product of the lengths of all the circles must be as large as possible (providing the numbers are all prime and different).

The only combinations of numbers that fit are (13,5,3) and (11,7,3).

13 * 5 * 3 = 195

11 * 7 * 3 = 231

Therefore the largest number of whistle blows is 231, with the circles arranged in circles of lengths 11, 7 and 3.

 Posted by Iain on 2004-03-19 14:10:55

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