The Puzzle: You are lost in a forest and reach a fork in the road.
- One path leads to a Safe Village, the other to a Lion’s Den.
- Two tribes live there: the Truth-Tellers and the Liars.
- You meet one person, but you don’t know which tribe they belong to.
- You can ask only one question. What do you ask to find the safe path?
1. The Strategy: The Double Negative
The trick is to ask a question that involves both possibilities, effectively creating an XNOR gate where the result is the same regardless of who you ask.
The Question:
“If I were to ask the other person which path leads to the safe village, which one would they point to?“
2. Why it Works
- Case 1: You are talking to the Truth-Teller. He knows the Liar will point to the wrong path. Since he tells the truth, he will report the Liar’s lie. Result: Wrong Path.
- Case 2: You are talking to the Liar. He knows the Truth-Teller will point to the right path. Since he must lie, he will point to the wrong path. Result: Wrong Path.
The Rule: Whichever path they point to, take the Opposite one.
Interview-Focused Questions
Q: How would you represent this in Boolean logic?
A: This is basically a NOT operator applied to a Truth value.
- T(L(x))={False}
- L(T(x))={False} Because there is only one Lie in the chain (either from the person you ask or the “quoted” other person), the final answer is always a Lie.
Q: Could you ask ‘If I asked YOU which path is safe…’?
A: Yes. If you ask “If I asked you tomorrow which path is safe?”, a Liar would have to lie about his lie, resulting in the truth. This is called the “Self-Composition” trick.
Key Takeaway
This puzzle is about Information Inversion. It’s a fundamental concept in security and protocol design.
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