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Takeaway Time

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

$35$ 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 and $9$ of the Chinese fans didn't like either Indian or pizza.
 
If all the teenagers liked at least one, how many liked only Indian?
 
 
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.