### The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

### Flippin' Discs

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

# Monkey Puzzle

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Three monkeys Barry, Harry and Larry met for tea in their favourite cafe, taking off their hats as they arrived.
When they left, they each put on one of the hats at random.
What is the probability that none of them left wearing the same hat as when they arrived?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.