Brain Teasers/Mislabeled Boxes of Marbles

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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?

Answer

Both

If you remove a marble from a box labeled both, you will get either white or black marble. Based on the the marble, you can determine the contents of all three boxes.

If BLACK is picked; the box labeled White can be either BLACK or BOTH. Since BLACK one is identified, White box should have BOTH. Thus Black box has WHITE marbles.

  • Both label: BLACK
  • White label: BOTH
  • Black label: WHITE

If WHITE is picked

  • Both label: WHITE
  • White label: BLACK
  • Black label: BOTH

If you pick a marble from White box or Black box, you can't determine whether the marble is from BOTH or the other color.

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