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If Tom takes 12 jelly babies he might take:
all 8 watermelon jelly babies and all 4 vanilla jelly babies, or
all 8 watermelon jelly babies and all 4 butter popcorn jelly babies.
So if he takes 12 jelly babies he cannot guarantee taking at least one of each flavour.
In each case the 4 remaining jelly babies will all be of the flavour he has yet to take, so taking one more jelly baby will ensure that he will have taken at least one of each flavour.
Therefore Tom should take 13 jelly babies.
Would You Like a Jelly Baby?
Age 11 to 14
ShortChallenge Level 
If Tom takes 12 jelly babies he might take:
all 8 watermelon jelly babies and all 4 vanilla jelly babies, or
all 8 watermelon jelly babies and all 4 butter popcorn jelly babies.
So if he takes 12 jelly babies he cannot guarantee taking at least one of each flavour.
In each case the 4 remaining jelly babies will all be of the flavour he has yet to take, so taking one more jelly baby will ensure that he will have taken at least one of each flavour.
Therefore Tom should take 13 jelly babies.
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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