Collecting Marbles
How many marbles need to be taken out to ensure that at least three are of the same colour?
Age
14 to 16
Challenge level
Problem
A bag contains hundreds of red, orange, green and blue marbles.
Marbles are drawn randomly from the bag, one at a time, and not replaced.
How many marbles must be taken out of the bag in order to ensure that at least three are of the same colour?
Student Solutions
If 8 marbles are chosen, it would be possible to have just two of each colour, and that would not fulfil the condition.
However, the ninth marble to be drawn would be the third of that colour, and so 9 marbles are needed to ensure that at least three are of the same colour.