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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?

In a Box

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

Chris and Jo decide to play a game.

They put two red and four blue ribbons in a box.

They each pick a ribbon from the box without looking (and without replacing them).

Jo wins if the two ribbons are the same colour and Chris wins if the two ribbons are a different colour.

Is the game fair?

If not, how many ribbons of each colour would you need in the box to make it a fair game?

Is there more than one way to make a fair game?


This problem is based on one offered by Doug Williams at the 2003 ATM conference in Bath UK. See also

Click here for a poster of this problem.