3 Mislabeled Boxes

You have three boxes. One has only red marbles, one has only blue marbles and the third has an equal number of red and blue marbles. The labels on the boxes have intentionally been switched so that each box is now marked incorrectly.

Your job is to relabel the boxes correctly. Of course you could just look in the boxes to find out which labels match, but can you do it without looking into each box? Reach into any one of the boxes and select one marble. Can you now correctly label all three boxes? If not, select a second marble from any box. What is the fewest number of marbles you need to inspect in order to correctly label each box?


You would only need to take out one marble because we know that all of the labels are incorrect.

So you pull one marble out of the box labeled “mixed.” If red comes out, you know that has to be the all-red box, so you put the red label on it. The box labelled “blue” must then be labelled “mixed” because you know it is also labeled incorrectly, and therefore can’t be blue.

You would label the last box “blue” because that is the only color/box combo left. If the first marble you pulled out from the box labeled “mixed” is a blue marble, then you solve the problem in the same general way.

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