### Pyramids

What are the missing numbers in the pyramids?

### Burning Down

One night two candles, one of which was 3 cm longer than the other were lit. The longer one was lit at 5.30 pm and the shorter one at 7 pm. At 9.30 pm they were both the same length. The longer one, burned out at 11.30 pm and the shorter one burned out at 11 pm. How long was each candle 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?

# Beans Eating Beans

##### Stage: 3 and 4 Short Challenge Level:
11

Pa Bean does not eat more than half the beans, so he eats at most 11 beans. Ma Bean eats the same number of beans as both children together, so she eats an even number of beans that is at least one quarter of the total number of beans eaten. Therefore she eats at least 6 beans. If she does eat 6 beans, then Pa Bean eats 11 beans, which is consistent with the information given. However, if Ma Bean eats 8 or more beans, then Pa Bean eats at most 7 beans and this is impossible as we are told that Pa Bean eats more beans than Ma Bean. So Pa Bean eats 11 beans.

This problem is taken from the UKMT Mathematical Challenges.
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