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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.*