Three people guard two doors. You know that:

- one person always tells the truth;
- one person always lies;
- one person randomly decides whether to tell the truth or lie (assume lies and truth are equally likely);
- the three know amongst themselves who they are.

This is an extension of the famous two person puzzle. Normally, you only have two guards, one tells the truth and one lies. You have to choose and open one of the doors, but you can only ask a single question to one of the guards.

What do you ask so you can pick the door to freedom?

In this case the solution is:

**If I asked what door would lead to freedom, what door would the other guard point to?**This works by considering the two possible outcomes. Namely:

- If you asked the truth-guard, the truth-guard would tell you that the liar-guard would point to the door that leads to death.
- If you asked the liar-guard, the liar-guard would tell you that the truth-guard would point to the door that leads to death.

This puzzle is so famous it's appeared many times in media

The inclusion of the trickster guard, however, changes the puzzle dramatically. Specifically, you questions have to work no matter who is being asked (truth-teller, liar, or trickster). Further, no matter what you ask, you always have to worry about the trickster screwing up your logic.

Thus, one strategy is to identify one person is NOT the trickster. We don't have to identify whether they are truth-teller, or liar.

Call the three gaurds A, B and C. You ask A:

"Is exactly one of these statements true:

If you get back the answer no, then the possibilities are:

Once you have found a person who is not the trickster, just point to a door and ask the person:

"Would your

Thus, reducing the problem to the previous case.

- You are the truth-teller
- B is the trickster

- A is the truth-teller and B is the liar (1. true, 2. false, so one statement true, so answer is yes which truth-teller truthfully gives)
- A is the trickster
- A is the liar and B is the truth-teller (both statements false so answer is no which liar lies about)

If you get back the answer no, then the possibilities are:

- A is the truth-teller and B is the trickster (both statements true, so answer is no which truth-teller truthfully gives)
- A is the trickster
- A is the liar and B is the trickster (1. false, 2. true so one statement true so answer is yes which liar lies about)

Once you have found a person who is not the trickster, just point to a door and ask the person:

"Would your

**exact**opposite say this door leads to freedom?"Thus, reducing the problem to the previous case.

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