### Burning Down

One night two candles were lit. Can you work out how long each candle was originally?

### A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

### Fair Shares?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

# Big Fish

##### Stage: 4 Short Challenge Level:

54kg

Let the weights in kilograms of the head and body of the fish be $h$ and $b$ respectively. Then $h = 9 + \frac{1}{3} b$ and $b = h+9$. So $b = 9 + \frac{1}{3} b + 9$, that is, $\frac{2}{3} b = 18$, which gives $b = 27$. Hence $h = 18$, so the whole fish weighed 54kg.

This problem is taken from the UKMT Mathematical Challenges.