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You're trapped in a room with 2 doors, one on your left and one on your right. One door leads to heaven, one door leads to hell. There are two birds in the room. One is a bad bird, which always lies, one is a good bird, which always tells the truth. You don't know which door is which, nor do you know which bird is which. The birds know which door is which.

You get to ask one question to one bird. How do you figure out which door leads to heaven?

This puzzle has some typical "expansions" to make it more difficult, like

You may not ask about the other bird

or equivalently (I think?)

There is only one bird which either always tells the truth or always lies.

From this expansion on, there is a post often going around online, considered a "troll post" (https://i.stack.imgur.com/lTQBa.jpg), which adds the following:

You may not use IF statements or any hypothetical statements in your question

I believe adding the restriction that forces a question to have a reply of either "true" or "false" does not change the difficulty, so let's work with that.

A solution I came up with the help from a stranger online, was asking the following question: "(Does the door on the left lead to heaven) XOR (Do you always speak the truth)"

My doubts about this are:

1) Is XOR not a hypothetical statement?

2) Would a lying bird lie about the entire question, or about the subquestions that are being XOR'd, or about all? (This may just be "definition"?)

3 Answers3

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In answer to 2): either type of bird could, and therefore presumably would, respond to the entire question. A lying bird would say "false" if the XOR statement evaluates to true, and vice versa. There's no issue here.

Question 1) is a little less straightforward. On the one hand, in logical terms XOR is a perfectly ordinary two-place truth-functional connective, just like AND and OR. And like those other two, it's symmetric: A XOR B means the same as B XOR A. Why would one think there's anything hypothetical about it?

On the other hand, A XOR B can be read as "A or B, but if A, then not B, and if B, then not A." Which really brings us back to the old problem of how to read "if-then." If we "If A, then B" as equivalent to "Either B, or else not-A" (this interpretation is called the material conditional), then we have something that's very easy to work with, but we have made it impossible to distinguish if-then statements from OR statements, because either form can be converted into the other. And since OR statements are interconvertible with AND statements, ... you see where this leads. No wonder the ban on IF statements is considered a trollish move.

StumpyLeg
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  • I see, thank you for the clarification... The "A or B, but if A, ..." is exactly what made me doubt whether XOR was allowed or not.

    I'm toying with the idea of rephrasing the question by "Is exactly one of the following statements true: '...' and '...'?" which should highlight the non-hypothetical nature of the question?

     –  May 29 '14 at 20:21
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what would the other bird say if you asked if the left door was heaven

user555648
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You should ask what the other bird would say and NOT take that door

Christosmag
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