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.