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I asked a friend the classic question about the two guards and two doors that goes as follows:

The rules are clear: there are two doors. One leads to the castle, the other, to certain death. You may ask one question – to one guard – to help you decipher which door is the correct one. It sounds simple enough, but there’s a catch: one guard always lies, and one always tells the truth.

His answer is to ask any guard, "is the truth telling guard in front of the castle door". And if the guard says yes he goes through that door, and if he says no then go through the other door.

Is this correct? I haven't heard it being answered like this before.

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This answer is correct, provided that they are standing in front of the doors (thanks for forcing the clarification @dcfyj). Take the following possibilities:

  1. The guard he talks to is a liar, and is in front of the castle door. He will respond "yes" to the question. This means that this is the correct door, because the truth-telling guard is not in front of the castle door.
  2. The guard he talks to is a liar, and is not in front of the castle door. He will respond "no" to the question. This means that this is not the correct door, because the truth-telling guard is in front of the castle door.
  3. The guard he talks to is honest, and is in front of the castle door. He will respond "yes" to the question. This means that this is the correct door, because the truth-telling guard is in front of the castle door.
  4. The guard he talks to is honest, and is not in front of the castle door. He will respond "no" to the question. This means that this is not the correct door, because the truth-telling guard is not in front of the castle door.

As you can see, every time the guard says "yes", whether it is the honest guard or not, the door you are standing at is the castle door. When the guard says "no", the other door is the castle door.

If they are not standing in front of the doors, a question that would provide the correct response would be, "Which door would the other guard tell me to go through?" You then go through the other door (not the one provided as the response).

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  • $\begingroup$ And if the guards aren't standing in front of the doors? $\endgroup$ – dcfyj Jun 14 '17 at 18:51
  • $\begingroup$ @dcfyj while he doesn't mention that the guards are standing in front of the doors, it is generally accepted as part of the question and is therefore implied. After all, why would a guard stand in front of a wall when there's a door to protect? $\endgroup$ – Moose Jun 14 '17 at 18:54
  • $\begingroup$ I have never assumed the guards were standing in front of the doors. Even if they're standing in front of the wall as long as they are within a close proximity to the door they could easily guard it. $\endgroup$ – dcfyj Jun 14 '17 at 18:56
  • $\begingroup$ Fair enough. I'll edit my response $\endgroup$ – Moose Jun 14 '17 at 18:58

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