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# Department of Science, Math, & Technology

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You are a prisoner.
Posted: Posted June 19th by Xhin
 You are a prisoner in a room with 2 doors and 3 guards. One of the doors will guide you to freedom and behind the other is a hangman - you don't know which is which. One of the guards always tells the truth. One always lies. One will always give a random answer. You don't know which one is which. You have to choose and open one of these doors, and you can ask 2 two yes-or-no questions in total. Both of these can be addressed to the same guard or to two different ones.
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Am I a male?

One will say yes, one will say no, and one will say a random answer.

Posted June 19th by S.O.H.
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Isn't this just an inverted Monty Hall problem?

Both of these can be addressed to the same guard or to two different ones.

Edited June 19th by Cruinn-Annuin
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I will just ask two of the 3.

Posted June 19th by S.O.H.
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If you ask the truth-teller and the random rando, they might both say yes. Now you've used up both of your questions without knowing anything other than who the liar is. If rando says no, then all you know is who the truth-teller is. You still know nothing about the doors and you have no questions left.

Posted June 19th by Xhin
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Xhin
Sky's the limit

If you ask a guard if both of the other guards would say that Door 1 is freedom, both the truth-teller and the liar will not be able to answer, as they don't know what the random answerer is going to say. Correct?

Posted June 19th by Cruinn-Annuin
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The questions have to have yes/no answers -- you can't ask recursive questions like "is your answer going to be yes" or ask the guards to predict the future ("Will my next answer be yes?") or inherent uncertainty ("Is randy the rando going to tell me the truth?")

Posted June 19th by Xhin
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Xhin
Sky's the limit

I'd select one of the guards and have him in my mind as I ask one of the other two something simple: "Am I a male?" Based on that guard's response, I'd either ask him or the third guard the following question: "Which door leads me to freedom?"

To explain further, let's say I decided to choose Guard #1. I'd then ask Guard #3 the simple question: "Am I a male?" If he answers yes, I know then that I'm talking to the guy telling the truth. If he answers with anything else, I'd then ask Guard #2 which door leads me to freedom.

Of course, this solution doesn't outright guarantee you freedom; even the original Monty Hall problem wasn't a 100% chance of success, as the MythBusters found when they tested it. It does, however, guarantee you the best chance of success.

Edited June 19th by Black Yoshi
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is fighting the guards an option'?

Posted June 19th by S.O.H.
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This reminds me of that "three lightbulbs" puzzle

Posted June 19th by Fox Forever
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I'd then ask Guard #3 the simple question: "Am I a male?" If he answers yes, I know then that I'm talking to the guy telling the truth.

Alternately he could be Randy the rando answering yes. You would then ask guard #3 "is door #1 freedom", Randy would give the random answer "yes" and you'd lose your head.

Posted June 20th by Xhin
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Xhin
Sky's the limit
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