mvictor wrote:

very tricky, and the wording is confusing.

23 of the same color must be left in the jar or outside?

if in the jar, then we need to take at least 21 out + 1 green and 32 blue or 21 white 24 green and 9 blue. but neither works, so it must be the case that we need to take out, and see if we have at least 23 of the same kind.

to make sure that we have 23 of the same kind, we need to take 21 white, 23 blue or green and 22 blue or green. this gives us a total of 66.

what is the source of this question?

Actually, the wording of the question is quite standard. How many do you need to take out to ensure that you have 23 of the same colour? means that out of the balls taken out, we need to ensure that there should be 23 of the same colour.

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