### Jewellery Boxes

When a jewel worth £5000 is transferred from one box to another, the average value of the jewels in both boxes increases. What is the total value of all the jewels?

### Algebraic Average

The mean of three numbers x, y and z is x. What is the mean of y and z?

### For Richer for Poorer

Charlie has moved between countries and the average income of both has increased. How can this be so?

# Pay Attention

##### Age 14 to 16 Short Challenge Level:

When a speaker gave a talk, 6% of the audience slept through the whole thing.
22% of the audience stayed awake and heard the entire talk.

Of the rest of the audience, half of them heard $\frac{2}{3}$ of the talk, and half of them heard $\frac{1}{3}$ of the talk.

What was the average proportion of the talk that people heard?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.