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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.

Jewelry Boxes

Stage: 3 Short Challenge Level: Challenge Level:1

Two boxes, P and Q, each contain 3 jewels.
When a jewel worth £5000 is transferred from P to Q, the average value of the jewels in each box increases by £1000.
What is the total value of all six jewels?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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