A jar has eight red, nine blue, and ten green marbles. What is the least number of marbles that you can remove from the jar and be certain that you have three of the same color?
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The least number of marbles that you can remove from the jar to be certain you have three of the same color is 10.
This is because if you remove 10 marbles, you could potentially remove 8 red marbles, leaving only one red marble in the jar. Then, you could potentially remove 1 blue and 1 green marble, leaving only one blue and one green marble in the jar.
However, since there are still two different colors remaining in the jar, you are not certain to have three of the same color.
Therefore, you would need to remove 10 marbles to be certain that you have three of the same color.
To find the least number of marbles that need to be removed to ensure that you have three of the same color, we can start by considering the worst-case scenario.
In this case, we want to minimize the number of marbles to be removed. So, we can assume that the first marble we pick is red. The second marble we pick will be blue (since there are more blue marbles than red marbles). Now, to make sure we have three of the same color, we need to pick a green marble.
To guarantee that we have three marbles of the same color, we need to remove one red, two blue, and three green marbles. Therefore, the least number of marbles we can remove from the jar and be certain to have three of the same color is 1 + 2 + 3 = 6 marbles.