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# Great logic problem watch

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1. (Original post by 3nTr0pY)
The OP's problem is really easy once you start thinking about it the right way.

Basically, all you need to know is:

Alternatively, you can ask "If I were to ask you which door to take to get to freedom, what would you say?"
And take that door...

as

= the same positive result whoever you ask!
wut
2. (Original post by tazarooni89)
You misunderstand me - When I say "combine the answers", I don't mean you ask questions and receive answers from both statues. I just mean you ask one statue a question about the answer that the other statue would provide. So you're taking advantage of both the fact that one always tells the truth, and the fact that the other one always lies.

You end up either receiving the truth about a falsehood, or a lie about a truth - and either way, this will lead you to the wrong door, so you just choose the other one.

So you're indirectly getting information from both, even though you only asked the question to one of them. That's what I mean by "combining the answers".
Ahhh I see! Sorry about that! I don't think it always combines the answers. For example...

Spoiler:
Show
If you asked "Does the guard of freedom tell the truth?" And you asked it to a truth-telling guard of freedom, they would answer yes truthfully and it wouldn't be combining the other guards lie-telling. So this question wouldn't combine both in all situations. I think.. I'm starting to confuse myself now lol. But for this solution, no matter which guard you ask, if they answer "yes", they are the guard of freedom and if they answer "no" they are the guard of death.
3. (Original post by tazarooni89)
As above. I think the idea is always going to be a case of combining the answers of the two statues to get an answer which is definitely false, since a positive and a negative will lead to a negative. Telling the truth about a false statement will lead you to a false statement. And telling lies about a true statement will also lead you to a false statement.
(Original post by tazarooni89)
You misunderstand me - When I say "combine the answers", I don't mean you ask questions and receive answers from both statues. I just mean you ask one statue a question about the answer that the other statue would provide. So you're taking advantage of both the fact that one always tells the truth, and the fact that the other one always lies.

You end up either receiving the truth about a falsehood, or a lie about a truth - and either way, this will lead you to the wrong door, so you just choose the other one.

So you're indirectly getting information from both, even though you only asked the question to one of them. That's what I mean by "combining the answers".
I misunderstood you again lol. I thought you meant you combine the truth-teller and the lie-teller every time, but it's not it's that you combine the truth/lie telling with the true/false statement you're asking about...

So asking about a true statement to a truth teller = true

So explained in maths it is...

(Original post by 3nTr0pY)
The OP's problem is really easy once you start thinking about it the right way.

Basically, all you need to know is:

Alternatively, you can ask "If I were to ask you which door to take to get to freedom, what would you say?"
And take that door...

as

= the same positive result whoever you ask!
Great logic! Loving it :-)
4. (Original post by mollster57)
If you asked "Does the guard of freedom tell the truth?" And you asked it to a truth-telling guard of freedom, they would answer yes truthfully and it wouldn't be combining the other guards lie-telling. So this question wouldn't combine both in all situations. I think.. I'm starting to confuse myself now lol. But for this solution, no matter which guard you ask, if they answer "yes", they are the guard of freedom and if they answer "no" they are the guard of death.
Surely this would only work if you knew from before that the statue guarding the door to freedom is the one which always tells the truth (or vice versa). I thought that in this particular problem, we're not supposed to know which is which?
5. (Original post by mollster57)
I misunderstood you again lol. I thought you meant you combine the truth-teller and the lie-teller every time, but it's not it's that you combine the truth/lie telling with the true/false statement you're asking about...

So asking about a true statement to a truth teller = true

So explained in maths it is...

Great logic! Loving it :-)
Yeah, I'm basically saying the same thing that 3nTr0pY is saying, just explained in words rather than numbers.

You have one truth teller and one false teller, so even though you don't know which is which, you're restricting yourself to one of the two possibilities I've highlighted above in bold, meaning you always get a false answer
6. (Original post by tazarooni89)
Surely this would only work if you knew from before that the statue guarding the door to freedom is the one which always tells the truth (or vice versa). I thought that in this particular problem, we're not supposed to know which is which?
Nope you don't know which is guarding what door. It assumes that each guard knows whether they are the guard of freedom or the guard of death, but you do not need to know whether the guard of freedom/death tells the truth or lies.

Remember "no" means the guard you are asking is guarding a death door, and "yes" means they're guarding a freedom door.

Imagine this:

1. Death door: Truth-teller, Freedom door: Liar
- If you asked the truth-teller at the death door "does the guard of freedom tell the truth?", he/she would tell the truth by saying "no" as the freedom guard is the liar. No = death door.
- If you asked the liar at the freedom door the same question, they would respond by saying "yes" because truthfully, the guard of freedom (themselves) doesn't tell the truth, but because of this, they lie - saying that they do. Yes = freedom door.

2. Death door: Liar, Freedom door: Truth-teller
- If you asked the liar at the death door "does the guard of freedom tell the truth?", they would lie and say "no". No = death door.
- If you asked the truth-teller at the freedom door the same question, they would tell the truth and say "yes". Yes = freedom door.

So there are four possibilities, on each one, if the guard answers "yes" they're guarding the freedom door and if the guard answers "no" they are guarding the death door.
7. (Original post by tazarooni89)
Yeah, I'm basically saying the same thing that 3nTr0pY is saying, just explained in words rather than numbers.

You have one truth teller and one false teller, so even though you don't know which is which, you're restricting yourself to one of the two possibilities I've highlighted above in bold, meaning you always get a false answer
Yep I see, but isn't that only with that particular question?
Isn't the one I just explained different? Because the statement is that "the guard of freedom tells the truth", if this is true, the guard of freedom is the truth teller and would answer "yes". Meaning that a truth is combined with a truth to equal a truth. Or in maths +1 x +1 = +1 (Yes, freedom door).

Yet, using the same question, it can combine answers to produce a false. If "the guard of freedom tells the truth" is false, the guard of death is the truth-teller and would answer "no". So a false is combined with a truth to equal a false. In maths -1 x +1 = -1 (No, death door).

Also, this same example can combine two falses to equal a truth. So if "the guard of freedom tells the truth" is false, the guard of freedom would answer "yes" (lying) so therefore two falses would be combined to equal a truth - Yes, freedom door.

.... I think lol, so confused right now
8. (Original post by mollster57)
Nope you don't know which is guarding what door. It assumes that each guard knows whether they are the guard of freedom or the guard of death, but you do not need to know whether the guard of freedom/death tells the truth or lies.

Remember "no" means the guard you are asking is guarding a death door, and "yes" means they're guarding a freedom door.

Imagine this:

1. Death door: Truth-teller, Freedom door: Liar
- If you asked the truth-teller at the death door "does the guard of freedom tell the truth?", he/she would tell the truth by saying "no" as the freedom guard is the liar. No = death door.
- If you asked the liar at the freedom door the same question, they would respond by saying "yes" because truthfully, the guard of freedom (themselves) doesn't tell the truth, but because of this, they lie - saying that they do. Yes = freedom door.

2. Death door: Liar, Freedom door: Truth-teller
- If you asked the liar at the death door "does the guard of freedom tell the truth?", they would lie and say "no". No = death door.
- If you asked the truth-teller at the freedom door the same question, they would tell the truth and say "yes". Yes = freedom door.

So there are four possibilities, on each one, if the guard answers "yes" they're guarding the freedom door and if the guard answers "no" they are guarding the death door.
Oh right I see, yeah that makes sense.
9. (Original post by tazarooni89)
Oh right I see, yeah that makes sense.
That one is slightly more confusing than some of the other solutions! I had to draw out the possibilities on paper to get my head round it to begin with haha!
10. (Original post by The_Last_Melon)
wut
Think of asking the truth teller as being a +1 action, leaving you with the correct result, and asking the liar as being a -1 action, leaving you with the wrong result.

What you want is the same, predictable choice of door, no matter who you ask. So you can either get them to refer to each other +1*-1 = =-1*+1 = -1 or themselves +1*+1 = -1*-1 = +1 to solve the problem.

(Original post by Mollster57)
Yep I see, but isn't that only with that particular question?
Isn't the one I just explained different? Because the statement is that "the guard of freedom tells the truth", if this is true, the guard of freedom is the truth teller and would answer "yes". Meaning that a truth is combined with a truth to equal a truth. Or in maths +1 x +1 = +1 (Yes, freedom door).

Yet, using the same question, it can combine answers to produce a false. If "the guard of freedom tells the truth" is false, the guard of death is the truth-teller and would answer "no". So a false is combined with a truth to equal a false. In maths -1 x +1 = -1 (No, death door).

Also, this same example can combine two falses to equal a truth. So if "the guard of freedom tells the truth" is false, the guard of freedom would answer "yes" (lying) so therefore two falses would be combined to equal a truth - Yes, freedom door.

.... I think lol, so confused right now
That one is really interesting because in a way you divided up the problem such that two properties were relevant - whether the guard is true and whether the guard is guarding the door to freedom. So now the space has 2*2 = 4 subspaces so to speak, making guaranteeing a reliable result slightly more tricky. Your way works by saying:

etc and assign a general state . By asking "does the guard to freedom tell the truth" you are essentially asking what the other guard will say except it is flipped if the guard you yourself are asking is a liar (and not flipped if he isn't). So we find for a state:

The response you get will be:

This works for general a and b. If you ask either possible guard of freedom you get:

And so you go down the door guarded by that guard if the guard says yes. Likewise you don't go down the door if the guard says no and take the other one instead.

Sheesh...that was harder than I thought....

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