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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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Racing Odds

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Nine or Ten?

Age 11 to 14 Short Challenge Level:

Convince yourself that when you roll two dice you are more likely to score 9 than 10.

If I roll 3 dice, which is more likely, a total score of 9, or a total score of 10?

You can find more short problems, arranged by curriculum topic, in our short problems collection.