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If there were just 7 green and 4 blue involved you would need to pick out at least 8, since this would cover picking out all the greens plus 1 blue. Any choice of less than 8 might produce only greens.

Now in the case where we have 7 green, 4 blue and 5 red marbles we would need to choose 7 + 5 + 1 = 13, since any number less than 13 could be covered by selecting (by chance) all the 7 greens and all the 5 reds with no blue at all.

In this case the answer is found by totalling all numbers other than the smallest, and then adding 1.

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Q: How many times do you need to pick from a bag to ensure that you have one of each color if there are 7 green 4 blue and 5 red marbles in a bag?
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