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Can You Solve the Scrambled Boxes Puzzle?

Mark Frauenfelder found this puzzle in the book My Best Mathematical and Logic Puzzles

Imagine that you have three boxes, one containing two black marbles, one containing two white marbles, and the third, one black marble and one white marble. The boxes were labeled for their contents – BB, BW, WW – but someone switched the labels so that every box is now incorrectly labeled. You are allowed to take one marble at a time out of any box, without looking inside, and by this process of sampling you are to determine the contents of all three boxes. What is the smallest number of drawings needed to do this?

Don't look in the comments if you are still working on it, because I believe someone will post the correct answer soon. -via Boing Boing

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Take one marble out of the "BW" box. The other marble in that box must be the same color, or the label will be correct. Suppose it's white. The "BB" box therefore must have one black and one white marble, or its label would be correct, and the "WW" box must have two black marbles. The same process of elimination can be extended if the marble you draw is black.
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