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Mislabeled Boxes of Marbles

Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you’re told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Which box should you remove a marble from to determine the contents of all three boxes?

The one labeled both. Since you know it’s labeled incorrectly, it must have all black marbles or all white marbles. After you determine what it contains, you can identify the other two boxes by the process of elimination.

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4 Comments on "Mislabeled Boxes of Marbles"


Agneau says
May 22, 2015 @ 12:01

Also possible to take a marble out of any box and then, knowing that all labels are wrong, determine the rest based on the colour of the one marble you took out.


Dan says
May 22, 2015 @ 12:17

@Agneau If you pull out a black marble from the box labeled white, you wouldn’t you know if it was actually the box of white marbles or the box with both colors. That’s why you can only pull from the box labeled both.


Hatem says
May 10, 2016 @ 23:00

If you take a marble from the mislabeled box “both” and found that it is white, this means the contents of this box could be white. This does not eliminate the possibility that it could have both black and white.

Assuming that the box labeled both does have only white marbles, the box labeled white could have both colours. in this case the box labeled black could have white will have black marbles.

The situation could be reversed. The box labeled black could have both colored marbles in it and the box labeled white could have both colored marbles in it.

Therefore, it is not possible to know for certain the contents of the boxes labeled white and black.


Dan says
May 11, 2016 @ 08:25

@Hatem If the box is mislabeled “both” and it has a color, by definition it can’t have both colors. It’s either black or white.


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