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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?

Weekly Problem 15 - 2007

Stage: 3 Challenge Level: Challenge Level:1

The 8 individuals will each wrestle 6 others. This suggests that the number of bouts is 8 x 6 = 48. However, each bout has been counted twice in this calculation, so the number of bouts is 48/2 = 24.

This problem is taken from the UKMT Mathematical Challenges.

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