The Puzzle: You have 3 jars containing Apples, Oranges, and a Mix of both.
- Each jar has a label: “Apples”, “Oranges”, or “Mix”.
- CRITICAL: Every single label is WRONG. How many pieces of fruit do you need to pick to correctly label all three jars?
1. The Strategy
The key lies in the fact that every label is wrong.
Step 1: Pick from the “Mix” jar
Since the “Mix” label is 100% wrong, this jar must either be pure Apples or pure Oranges.
- Let’s say you pick one fruit and it’s an Apple.
- Conclusion: The “Mix” jar is actually the Apples jar.
Step 2: The Deduction
We now have two jars left, labeled “Apples” and “Oranges”.
- We know the real “Apples” jar is already found.
- The jar currently labeled “Oranges” cannot be oranges (because all labels were wrong).
- Therefore, the jar labeled “Oranges” must be the Mix jar.
- It follows that the jar labeled “Apples” must be the Oranges jar.
2. Result
You only need to pick ONE fruit from the jar labeled “Mix”.
Interview-Focused Questions
Q: Why start with the ‘Mix’ jar?
A: If you started with the ‘Apples’ jar and found an orange, the jar could be either “Oranges” or “Mix”. You wouldn’t be sure. But because the ‘Mix’ label is wrong, it guarantees you find a pure-fruit jar, which collapses the remaining possibilities.
Q: Is this a probability puzzle?
A: No, it’s a Deduction puzzle. It’s about using a known negative (the labels are wrong) to create a positive certainty.
Key Takeaway
This puzzle tests your ability to identify the most informative starting point in a logical system.
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