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The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

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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.

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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 37 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1
There are six different possible ways of choosing two of the loose ends. Only two of these possibilities lead to a loop being made, therefore the probability that Sam holds one tied loop is $\frac{2}{6}=\frac{1}{3}$.

This problem is taken from the UKMT Mathematical Challenges.

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