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Takeaway Time

Age 14 to 16 Short Challenge Level:

$35$ teenagers were asked what takeaways they liked to eat.
 

$24$ answered Chinese
$16$ answered Indian
$10$ answered pizza

None of the teenagers liked all three.
All who liked pizza also liked Chinese.
$9$ of the Chinese fans didn't like either Indian or pizza.
 
If all the teenagers liked at least one, how many liked only Indian?
 

 

 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.