Three Box Puzzle Brain Teaser

Solution:

1. Pick a ball from the box labeled “one red and one blue.” Since all boxes are labeled incorrectly, this box cannot have one red and one blue ball. It must either have two red balls or two blue balls.

2. Observe the color of the ball you picked:

• If the ball is red, the box must contain two red balls.
• If the ball is blue, the box must contain two blue balls.

3. Relabel the box you just picked from:

• If you picked a red ball, relabel this box to “two red balls.”
• If you picked a blue ball, relabel this box to “two blue balls.”

4. Relabel the other two boxes:

• Since the original label “one red and one blue” is now taken by the box you just correctly labeled, the box originally labeled “two red balls” must contain one red ball and one blue ball (because it was labeled incorrectly).
• The remaining box, which was originally labeled “two blue balls,” must now be correctly labeled as the box with the remaining color combination.

5. Check the final labeling:

• If you picked a red ball:
  • The box labeled “one red and one blue” now contains two red balls.
  • The box labeled “two red balls” now contains one red and one blue ball.
  • The box labeled “two blue balls” now contains two blue balls.
• If you picked a blue ball:
  • The box labeled “one red and one blue” now contains two blue balls.
  • The box labeled “two blue balls” now contains one red and one blue ball.
  • The box labeled “two red balls” now contains two red balls.