Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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?
This problem is taken from the UKMT Mathematical Challenges.