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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?

Colour Building

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Pick any colour of rod. Consider how many different ways there are to make it with a white rod on the right-hand end, and how many ways there are with a red rod on the right-hand end.