### Bat Wings

Three students had collected some data on the wingspan of some bats. Unfortunately, each student had lost one measurement. Can you find the missing information?

### 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?

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:

Suppose that initially the total value of the jewels in $P$ is $£A$, and those in $Q$ is $£B$.

The average value in $P$ at the start is $\frac A3$. After the jewel has been moved it is $\frac{A-5000}2$. Therefore:

\frac A3 = \frac{A-5000}2 - 1000

Multiplying by $6$ and collecting like terms gives $A = 21000$.

The average value in $Q$ at the start is $\frac B3$. After the jewel has been moved, the average value is $\frac{B+5000}4$. Therefore:

\frac B3 = \frac{B+5000}4 - 1000

Multiplying by $12$ and collecting like terms gives $B = 3000$.

Therefore the total value is $£24,000$

This problem is taken from the UKMT Mathematical Challenges.
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