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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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 No Subject | Comment 19 of 30 |

If each circle must contain one, and only one, start of an arrow and end of an arrow, then the circles  must be arranged to form a large, closed shape.

Meaning, that the monkeys will just jump from one circle to the next, around the outside of the shape.  So, twenty-one circles means twenty-one jumps for the monkeys to get back to their own circle, so 21 whistle blows.

 Posted by Lisa on 2004-04-20 18:07:12

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