This puzzle is always presented as difficult, but why not just ask a known? If your eyes are brown just ask “Are my eyes brown?” You’d immediately know which one lies or tells the truth.
Then you still don’t know which door is the correct one, you’ve just learned which guard tells the truth and you’ve used up your one question. The trick is to ask which door the other guard would tell you is the correct one and then go through the other door. If you’ve asked the lying guard, they’ll lie about what the honest one would say and point you towards the wrong door. If you asked the honest one, they’ll truthfully tell you what the lying guard would say and also point you towards the wrong door
Because there are two doors and only one question. If you ask a known question unrelated to the door you find out who the liar is but lose your opportunity to ask them which is the correct door.
The difficulty comes from only being able to ask one question. It’s very easy to figure out the liar, but it’s much more difficult to figure out the liar and the correct door in the same question
In fact, the lying guard is a red herring. You get one question, and need one piece of info: the door. The canonical question doesn’t tell you which guard lies, nor do you care to find out.
This puzzle is always presented as difficult, but why not just ask a known? If your eyes are brown just ask “Are my eyes brown?” You’d immediately know which one lies or tells the truth.
E: I missed the limit of one question.
Then you still don’t know which door is the correct one, you’ve just learned which guard tells the truth and you’ve used up your one question. The trick is to ask which door the other guard would tell you is the correct one and then go through the other door. If you’ve asked the lying guard, they’ll lie about what the honest one would say and point you towards the wrong door. If you asked the honest one, they’ll truthfully tell you what the lying guard would say and also point you towards the wrong door
Knowing who lies and who tells the truth doesn’t tell you which door leads to the prize and which to death.
Because there are two doors and only one question. If you ask a known question unrelated to the door you find out who the liar is but lose your opportunity to ask them which is the correct door.
The difficulty comes from only being able to ask one question. It’s very easy to figure out the liar, but it’s much more difficult to figure out the liar and the correct door in the same question
In fact, the lying guard is a red herring. You get one question, and need one piece of info: the door. The canonical question doesn’t tell you which guard lies, nor do you care to find out.