### A Dicey Paradox

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.

### Nines and Tens

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

### Squaring the Circle

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

# The Lady or the Lions

##### Stage: 3 Challenge Level:

Whenever the peasant has to make a choice of which way to go he has 3 choices and no way of knowing which route to take. Assume he chooses randomly and work out the probability of him reaching chamber A and the probability of him reaching chamber B. The clever princess has seen the map and worked out which chamber he is more likely to end up in so she waits there knowing that then the story is more likely to end up happily ever after.

Xing Cong gave the solution that the princess should wait in A because the probability of the peasant arriving in A is 5/9, and he sent this diagram.