Of two doors, one leads to freedom, the other to danger
Of two doors, one leads to freedom, the other to danger. A guard stands at each door — one always tells the truth, the other always lies, but you do not know which is which. You may ask only one guard a single question. Meet thinks that without knowing who the liar is, there is no way to be certain of the right door. His sister says there is one clever question that always works. Who is right?
Who do you think is right? Pick one.
The answer: His sister is right — ask "if I asked the other guard which door leads to freedom, what would he say?"
Why
Meet's worry makes sense on the surface — one guard's answer alone cannot be trusted, since you have no way to know if you happened to ask the liar. The trick is to ask a question that FOLDS IN the other guard's answer, so both guards, despite being opposite in every other way, are forced to give the identical (wrong) answer. Asking the truthful guard 'what would the OTHER guard say' gets you an honest report of a lie — he truthfully tells you the liar's false answer, pointing to the danger door. Asking the LYING guard the same question gets you a lie about a truth — he dishonestly reports the opposite of what the truthful guard would really say, which is also the danger door. Test it: no matter which guard you happen to ask, the reported answer always points to the WRONG door — so the real answer is simply to walk through the OTHER door, the one not mentioned. His sister is right: asking about what the other guard would say cancels out exactly one truth and one lie, so both guards end up giving you the same, reliably wrong answer — pointing you straight to the right door by elimination.
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