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Answer: 11
Using a table
2 children together eat the same as Ma Bean
Using reasoning
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.
Eating Beans
Age 11 to 14
ShortChallenge Level 
Answer: 11
Using a table
2 children together eat the same as Ma Bean
| Ma Bean | 2 | 6 | 8 | ||
|---|---|---|---|---|---|
| Ma + 2 children | 4 | 8 | 12 | 16 | 20 |
| Pa Bean | 19 | 15 | 11 | 7 | 3 |
| Comment | Pa eats more than half | Good | Ma eats more than Pa | ||
Using reasoning
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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