The challenge
One door is safe and one is not. One guard always lies and one always tells the truth. You may ask one guard one question. What do you ask to choose the safe door?
Two Guards and Two Doors Puzzle
Solve this medium logic challenge, then compare your reasoning with the hint, checked answer, verification, and variation.
Hint
Make either guard report the other guard's answer.
Ask what the other guard would say
Truthful and lying cases
- Ask either guard which door the other guard would call safe.
- The truthful guard reports the liar's unsafe choice, while the liar reverses the truthful guard's safe choice.
- Both cases indicate the unsafe door, so choose the opposite one.
Ask either guard, 'Which door would the other guard say is safe?' Then choose the opposite door. The truthful guard accurately reports the liar's wrong choice; the liar falsely reports the truthful guard's correct choice. Both point to the unsafe door.
Two-case truth table
Write the truthful-respondent and lying-respondent cases separately. Each points to the same unsafe door before the final reversal.
A direct question depends on guard identity
Asking a direct question leaves the answer dependent on which guard was chosen. The question must neutralize that unknown identity.
Transform unknown identities into one stable result
Compose two uncertain transformations so they produce one predictable result.
How confident were you?
Make both cases point to the same door
Build a two-case table. Ask what each guard would say about the other guard's answer, then look for a result that is identical whether the respondent lies or tells the truth.
Rewrite the solution as a yes-or-no question
Can you write a yes-or-no question about one named door that also works? Verify it against both possible guard identities.
Study truth-teller and liar puzzles for the reusable method behind this challenge. Then explore the logic puzzles and deductive reasoning learning path for connected examples and practice.