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A friend posed this puzzle to me a few months ago, and it has tortured me ever since. The puzzle goes something like this:

Suppose you're on a gameshow, and there are three doors: two doors have a goat, and one door has a car. There are also two lights: one red, and one green. If you ask any yes or no question, one of the lights will go off indicating a yes/no answer. The problem is you don't know which light is "yes" and which light is "no." If you are able to ask two questions, what questions should you ask so that you always get the car?

I've come up with a few "strategies" to the problem. For instance, if I ask "does door 1 have a goat?" and "does door 2 have a goat?" and the same light goes off both times, the car must be behind door 3. This breaks though if different lights go off, since I'd then know the car must be behind door 1 or 2, but I can't be sure of which one. I could also use my first question to determine which light is yes and which is no by asking "is my name Glare?" but then it's not possible to locate the car with my remaining question (is it?).

A solution would be appreciated, but if there is something really obvious that I'm not seeing, a hint would be nice too.

EDIT: I know this is similar to the Monty Hall problem, but I assure you that this is how the problem was given to me. In the event that my friend was lying about the existence of a winning strategy, could someone prove that a solution does not exist (for my peace of mind)?

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    $\begingroup$ Seems like an interesting variation of the monty Hall problem $\endgroup$ Commented Jan 18, 2015 at 3:30
  • $\begingroup$ I think it is the Monty Hall problem, but with a flawed conclusion...it's not actually possible to get the car every time I don't think. If I remember correctly, the problem is really concerned with your probability of winning the car. Or am I mistaken? $\endgroup$ Commented Jan 18, 2015 at 3:32
  • $\begingroup$ When my friend gave this problem to me he said a winning strategy existed. I don't believe he was lying to me... $\endgroup$
    – Glare
    Commented Jan 18, 2015 at 3:34
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    $\begingroup$ I think this question should be moved to puzzling.stackexchange.com $\endgroup$
    – square_one
    Commented Jan 18, 2015 at 3:37
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    $\begingroup$ This question has been flagged twice for migration to puzzling.SE. While I acknowledge that this probably would be on-topic there, the history of Math.SE shows that this kind of a question is also on-topic here. Therefore I won't initiate migration at this time. We have a bit of history about some questions possibly being better fits for a new sister site, but I don't remember whether a conclusion was reached. That should IMO be discussed in meta. Do search for old meta threads! $\endgroup$ Commented Jan 18, 2015 at 8:14

1 Answer 1

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You can ask, "If someone asked if the car is behind door 1, would the green light light up?"

If green means yes and the car is behind door 1, then the green light will light up. If green means yes, but the car is behind another door, the red light will light up.

If green means no and the car is behind door 1, the green light will light up for no. If green means no and the car is behind another door, the red light will light up for yes.

Thus with this question we can figure out if the car is behind door 1 or not. Then we can ask, "If someone asked if the car is behind door 2, would the green light light up?" This will give us all the information we need.

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