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Three boxes riddle - the age old logic puzzle

Solve the Classic Three Boxes Puzzle with Elementary Logic

Solve the Challenging Three Boxes Riddle (the Solution Covers all Possibilities)

Three boxes puzzle: You have 3 boxes of colored balls. All 3 boxes are wrongly labeled. Open only one box, pick one ball and correctly label the boxes.

The puzzle

Labels of the three boxes with closed lids are BB, BR and RR. The boxes have colored balls inside. One box has only Blue, the second only Red, and the third—Red and Blue mixed.

The label BB should mean, only Blue balls are in the box. Label RR should mean, only Red balls are inside and label BR should mean the box has balls of both Blue and Red colors.

The problems is—all the boxes are wrongly labeled.

Three wrongly labeled boxes

Your job is to open just one box, take out only one ball and tell the color of the balls in each of the three boxes in 10 minutes.

You just can't open a box randomly and find the answer, can you? Give it an honest try. It won't be hard to solve.

We'll not leave you high and dry. The step by step solution covers all possibilities.

Easy to Understand Solution to the Classic Three Boxes Riddle

Step 1: Understand the puzzle clearly (problem definition)

You know:

  • The labels on three boxes are: BB (meant for Blue only), BR (meant for Blue and Red), and RR (meant for only Red).
  • Each box actually contains only Blue balls, only Red balls, or a mix of both.
  • But, all the labels are incorrect. For example, BB box should have contained, but doesn't contain, only Blue balls.

Step 2: Key Insights and Conclusion from a mental experiment

Imagine opening the BB or the RR labeled box. Possibilities are:

  • If you found a Blue ball in the BB box, you would know for sure it contains a MIX of Blue and Red balls (as it cannot contain only Blue balls by puzzle condition and also it cannot contain only Red balls by actual observation).
    • Instead, if you found a Red ball in BB box, you won't be sure if the box contained only Red or a mix of Blue and Red. Uncertainty.
    • Overall result: You would not be certain of the contents of the three boxes by opening the BB box and picking one ball (that might be blue or red).
  • Same way, opening the RR box and picking one ball cannot make you certain of color of balls in all three boxes.
  • Conclusion: If you can't solve the riddle by opening two boxes, you have only one choice leftyou have to open the remaining BR box and deduce all three box contents.

Have a look at the implication diagram at the end. It highlights the uncertainty of opening up either of BB or RR labeled box.

Step 3: Solve by Opening BR Box to first deduce contents of BR Box

Open the BR labeled box (supposedly it should contain Blue and Red mixed, but actually it doesn't). Two possibilities. You found:

  • A Red ball: If the ball is Red, then the BR box actually contains only Red balls.
  • A Blue ball: If the ball is Blue, then the BR box actually contains only Blue balls.

Step 4: Deduce Contents of All Three Boxes

You already deduced the color of balls in the BR box (only Red or only Blue). Based on this color, use logic to determine the contents of the other two boxes.

Work out yourself the logic behind deduction of contents of other two boxes. It will be fun!

Hint: If the BR box contains all Red, the BB box must contain Blue Red mixed as it cannot contain all Blue.

This solution makes it certain that opening only the BR labeled box to pick one ball will give you the solution.

You have used structured logic deduction to solve the puzzle.

Highlighting the uncertainty in opening either of BB or RR box

Following implication diagram should help visualize part of logical deduction for solving the riddle.

Implications flow diagram


More puzzles to enjoy

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Enjoy puzzle solving while learning problem solving techniques.