I am having a problem answering this math problem.

Andrea has a box of marbles in it. She has seven red marbles, thirteen blue marbles and nineteen yellow marbles. If she reaches in and takes out marbles without looking, what is the fewest number of marbles she will need to take out to guarantee that she has three the same colour?

39 = total marbles.
7/39= red marbles.
13/39= blue marbles.
19/39= yellow marbles.

Now I am stuck, do I have to build a graph and if so how, sorry I am so confused with this problem.
Thanks for your help.

She might draw out two of each color. There are only three colors, so on the 7th marble, it must be the same color as two of the others. So, with 7 marbles, she is sure to have 3 the same.

How many of each color are in the box doesn't matter. Only the number of colors.

Thanks again๐Ÿ˜€

To solve this problem, you don't need to build a graph. Instead, let's think about it logically.

To guarantee that Andrea has three marbles of the same color, we want to find the scenario where she has taken out the minimum number of marbles and still doesn't have three of the same color.

Let's consider the worst-case scenario. In this scenario, Andrea picks out two red marbles, two blue marbles, and two yellow marbles. So far, she has already taken out six marbles, and she does not have three of the same color yet.

Now, for her seventh marble, no matter what color it is, she will have three marbles of the same color. Therefore, the fewest number of marbles she will need to take out to guarantee that she has three marbles of the same color is seven.

So, the answer to the problem is seven.

I hope that helps! Let me know if you have any further questions.