# How many marbles must you take out in order to be certain of getting two of the same colour?

I came across this question as a part of a practice test I'm working on to prepare for a maths exam at school:

An urn contains 4 red, 6 blue, 3 green, 8 brown and 9 white marbles. The urn has a lid and you can't see into it. How many marbles must you take out in order to be certain of getting two of the same colour?

I think this problem would be solved by using probability theory but wasn't able to find a way to do it. My initial thinking was that since 3 is the smallest of the coloured marbles that if I picked 2 then it would give me at least two green marbles but then there's the issue of not getting 2 of green when picking.

• If you have pulled out $5$ marbles, what is the only way that you don't have two of the same color? When they are all different colors, each of the colors represented once a piece. If you are in this scenario and you pull out a sixth marble... what happens? Jan 28 at 6:13
• en.wikipedia.org/wiki/Pigeonhole_principle Jan 28 at 6:13