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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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Nine or Ten?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Non-transitive Dice

Age 11 to 14 Challenge Level:
If Charlie picks the green die, what should Alison do?
If Charlie picks the red die, what should Alison do?
If Charlie picks the blue die, what should Alison do?