Heaven and hell: two doors
Two doors: one leads to heaven, one to hell. Each door has a guard—one always tells the truth, one always lies (you do not know which is which).
You may ask one guard exactly one yes/no question, then you must choose a door and walk through it.
What should you ask to guarantee you enter heaven?
Pick either guard and ask:
“If I asked the other guard which door leads to heaven, which door would he point to?”
Then go through the other door—the one he did not indicate. That door is heaven.
Why it works
Label heaven H and hell D. You only care which door he points to, then invert.
Case 1: you ask the truth-teller (T)
He reports honestly what the liar (L) would do if asked about heaven.
- L would lie and point to D.
- T says: “He would point to D.”
You invert → choose H ✓
Case 2: you ask the liar (L)
The embedded question is: “If I asked T which door is heaven, what would T say?”—T would say H.
- L lies about that and answers: “He would point to D.”
You invert → choose H ✓
Either way the answer names the hell door; inverting always gives heaven.
Equivalent wording
Some versions use:
“If I asked you which door is heaven, which door would you point to?”
Then go through the door he does point to (no inversion).
- Ask T: points to H.
- Ask L: lies about “I would point to H,” still points to H.
Both phrasings use a double layer of “who would answer what” so truth and lies collapse to the same useful action.
Takeaway
You never need to identify which guard is which—only to ask a question whose answer always encodes the wrong door, then flip it (or use the symmetric variant).