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Painting Cubes

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?

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Lesser Digits

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

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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?

Coins

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

British coins in current circulation are:
1p (penny)
2p
5p
10p
20p
50p
£1 (=100p)
£2

Start by considering individual clues and how they restrict the possibilities.