Would you like a jelly baby?
What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
Age
11 to 14
Challenge level
Problem
In Tom's pocket there are 8 watermelon jelly babies, 4 vanilla jelly babies and 4 butter popcorn jelly babies.
What is the smallest number of jelly babies he must take out of his pocket to be certain that he takes at least one of each flavour?
Student Solutions
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.