Three boxes riddle - the age old logic puzzle

Tro to Solve the Challenging Three Boxes Riddle: Go through the Solution that 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.

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.

Comment

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. Here goes the easy to understand solution (only a little bit of the logic mystery still left for you to unravel).

Easy to Understand Solution to the Classic Three Boxes Riddle

Step 1: Write down the Information for Clear Understanding

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.
• Crucially, all the labels are incorrect. For example, BB box should have contained, but doesn't contain, only Blue balls.

Step 2: What are the Key Insights and Deductions from the Given Information?

Imagine the possibilities of opening the BB or the RR box.

• Opening the BB labeled box would not be helpful: 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.
• Overall result: You would not be certain of the contents of the three boxes by opening the BB box (as the color of the single ball you picked might be Red or Blue).
• Same way you will face uncertainty if you open the RR box.
  
• Conclusion: If you can't solve the riddle by opening two boxes, you have only one choice left—you have to open the remaining BR box and deduce all three box contents.

If you want, have a look at the implication diagram at the end that 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

Let's 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). Now, based on this color, you can use logical deduction 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.

[ Consider: If you decided to analyze the case of opening the BR box first, you would have become sure that you would be able to deduce the contents of all three boxes, but you would not be sure whether that would also be true for opening the BB or RR box. ]

Conclusion

By opening only the BR box and analyzing the chosen ball's color, you can successfully determine the contents of all three boxes!

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.

---

Puzzles you may enjoy

Easy to hard categorized brain teasers with systematic solutions from SureSolv.com:

Challenging brain teasers with solutions: Long list.

And for more puzzles, here are a few other websites with rich collections of easy to hard puzzles:

1. BrainDen: Offers a variety of puzzles, including grid-based puzzles, riddles, and more. They categorize puzzles by difficulty, making it easy to find ones that suit your level.
2. Puzzle Baron: Provides a wide range of puzzles sorted by difficulty.
3. BrainBashers: Offers a collection of logic puzzles, brain teasers, and other mind-bending challenges sorted by difficulty.
4. MathsisFun: While primarily focused on math, MathsisFun has puzzles suitable for all ages. They range from simple to challenging.

Good luck to your problem-solving journey!

---