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Logic Outside the Box(es)

Imagine you have three boxes, one containing two blue marbles, one containing two red marbles, and the third has one blue marble and one red marble. The boxes were labeled for their contents: BB, RR, and BR. Then, someone switched the labels so that every box is now labeled incorrectly.

You are allowed to take one marble at a time out of any box, without looking inside. By this process of sampling, you are to determine the contents of all three boxes.

What is the smallest number of samples needed to do this?


Hint: Set up the situation and test it physically, carefully drawing random marbles from random boxes...and thinking carefully about what you know and do not yet know.


Solution Commentary: Only one sample is needed...out of the box mislabeled BR. If the marble is red, what do you know...Think carefully, and the contents of all three boxes should fall into place.