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What are the missing numbers in the pyramids?

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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?

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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: Challenge Level:1

The Bean family are very particular about beans. At every meal all Beans eat some beans. Pa Bean always eats more beans than Ma Bean but never eats more than half the beans. Ma Bean always eats the same number of beans as both children together and the two children always eat the same number of beans as each other.

At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?


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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