Use Elementary or Advanced Logic to Solve the Classic Riddle
You have three wrongly labeled boxes BB, BR, and RR. Each contains colored balls (Blue, Red, or both). Pick a ball from one box to correct the three labels.
The Classic Three Boxes Logic Puzzle
Three boxes labeled BB, RR and BR contain colored balls—Blue, Red and both. Label BB indicated only Blue, RR only Red and BR both colors. Someone switched the labels. Now all labels are wrong. Pick a ball from one box to correct the labels.
Can you solve this challenging logic puzzle in 5 minutes?
Additional challenge: Solve the logic puzzle in more than one way.
Hint: Decide how to proceed—the strategy and then logic analysis. This will speed up the solution.
Solutions to the Classic Three Boxes Riddle
Understand the puzzle
- Three boxes contain Blue balls, Red balls, or a mix of both.
- The labels on the three boxes are: BB (for Blue), BR (for Blue and Red), and RR (for Red).
- All labels are wrong.
- To solve: Choose one box, pick one random ball from the box and tell what each box contain.
Apply advanced logic to solve Immediately without going into details
- Fact: The picked ball may be Blue or Red whichever box I choose.
- ⇨ In both cases, the conclusion must be correct with certainty in the solution.
- ⇨ Choice of the correct box will ensure certainty of the solution.
- Fact: By the nature of the labels and intended content, the boxes BB and RR are both the same. Possible results and the conclusions for one will apply equally well to the other.
- ⇨ If BB were the correct box, the RR box would also be the second correct box with certainty.
- ⇨ This violates the fundamental rule of a unique certainty and solution in a well-formed logic problem.
- ⇨ Both the BB and the RR boxes are the wrong boxes to choose.
- ⇨ I will choose the BR labeled box to guess the contents in the three boxes correctly.
Possible results of picking one ball from the BR box:
- Color of ball Blue
- ⇨ The BR box must contain Blue balls (it cannot be Blue and Red because its label is wrong—it could either be all Blue or all Red).
- ⇨ The RR box cannot be all Blue (BR box already contains Blue) or all Red (wrong label). So, the RR box contains Red and Blue balls.
- ⇨ The remaining BB box contains all Red balls.
⇨ Logic for picking a Red ball from the BR box is similar in certain identification of the box's contents.
Takeaway:
Without going through the possibilities and conclusions of choosing the correct box, it is chosen by pure logic.
Second Solution to the Classic Three Boxes Riddle: Strategy and Elementary Logic
Fact: The logical process in analyzing the case of choosing the BB box will be similar to choosing the RR box with the same results—success or failure. If I analyze one, the other can also be analyzed easily, and both the results will be the same.
⇨ Strategy: Results and conclusions will be analyzed for the BB and BR boxes (saving the unnecessary effort of analyzing the RR box).
Thought Experiment: A random ball picked from the BB box
- Color of ball Blue: The BB box must contain Blue and Red balls, the RR box contains Blue balls and the BR box contains Red balls ⇨ Certainty ⇨ Success (deduce the reasons yourself).
- Color of ball Red: The BB box may contain all Red balls or Blue and Red balls ⇨ Uncertainty ⇨ Failure.
- ⇨ Choice of BB box cannot ensure certainty in the correct guess, when in one case, a correct guess is uncertain.
- ⇨ BR box must be chosen for correct guess.
Imagine: A random ball picked from BR box
- Color of ball Blue: The BR box has Blue balls, the BB box has Red balls and the RR box Blue and Red balls ⇨ Certainty ⇨ Success.
- Color of ball Red: The BR box has Red balls, the BB box has Blue and Red balls and the RR box Blue balls ⇨ Certainty ⇨ Success.
Both color possibilities resulting in success verified the correct choice of the BR box for solving the logic puzzle.
Third Solution By Visual Logic Analysis
Logic analysis of RR box chosen (avoiding unnecessary analysis of BB box):
Similar logic analysis rejects the choice of the BB box. The only box to choose for one random ball to pick up is the BR box.
Logic analysis for correct identification of contents of all three boxes by choosing the BR box:
Takeaway
It is widely known, visual representation increases clarity in understanding. In this solution of the classic three boxes logic riddle, visual representation did both—increased clarity and also did the logic analysis.
Questions for you
- Which solution do you like most?
- Which solution provided you the maximum food for thought?
- Did any part of the reasoning surprise you? If so, why?
- How would you explain one of these solutions to someone else?
- What other puzzles or problems do you think this kind of reasoning could apply to?
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Enjoy puzzle solving while learning problem solving techniques.