First Puzzle : The Monkey Dance

Ok friends, Hi I am Mayank Gupta......Thanks first of all to Sajal for inviting me to this blog....he must have surely been in a state of hypnotism when he sent an invite to a dunce like me.......

So I start with one of my favourite puzzles....well it came in ZIO 2005:
The director of Hind Circus has decided to add a new performance called the monkey
dance to his show. The monkey dance is danced simultaneously by N monkeys.
There are N circles drawn on the ground. There are N arrows drawn between the
circles in such a way that for each circle, exactly one arrow begins at that circle and
exactly one arrow ends at that circle. No arrow can both begin and end at the same
circle.
When the show begins, each monkey sits on a different circle. At each whistle of the
ringmaster, all the monkeys simultaneously jump from one circle to the next, following
the arrow leading out of the current circle. This is one step of the dance. The dance
ends when all the monkeys have simultaneously returned to the circles where they
initially started.
The director wishes the dance to last as many steps as possible. This can be achieved
by drawing the arrows intelligently.
For each of the three values of N given below, what is the maximum number of steps
that the monkey dance can be made to last by drawing arrows appropriately?

(a) 9 (b) 12 (c) 15

Sajal: Don't ans since u already know the soln.

Level : Difficult