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## Question

Yesterday this hoary old question was put up:

"There are two gatekeepers each standing in front of a gate going towards hell or heaven

and one of them is a truth-teller and one of them is liar and you don't know that who is

true or who is lying ,so just by asking one question(ONLY ONE) to any one of them(NOT BOTH)

how can you find out the way to heaven"

and of course the poster was made aware that the answer is well-known.

But wait. Nobody said that each gate-keeper knows whether the other one is a liar or truthful.

So can you still ask one question to get to heaven? (Or hell if that's your choice.)

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The way to heaven is guarded by a truth teller. Therefore ask them something like, "How many fingers do I have?" However, as some may disagree with this, perhaps it should be in the paradox section?

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OK, let me try to make it even a more general setting - assume both gatekeepers are either liars or truth-tellers (so they can both be liars, both truth-tellers, or one a liar and one a truth-teller).

Then

Ask anyone of them "If I were to ask you if your gate allows passage to heaven, would you say yes?".

Double negation shows that:

- a truth-teller will answer YES if the gate allows passage to heaven and NO if the gate allows passage to hell

- a liar will always answer YES if the gate allows passage to heaven (to cover up the fact that if you had simply asked him "Does this gate allow passage to heaven", he would have to lie and say NO) and NO if the gate allows passage to hell (again, covering up his answer for the "Does this gate allow passage to heaven" question)

So, regardless of their type: choose that gate if answer is YES, choose the other if answer is NO.

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doesnt each one know what he is? Therefore they know what the other it. It is still the same.

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Darth, "The way to heaven is guarded by a truth teller." Who told you that? It wasn't me. Maybe it was the liar!

Aaryan, noone told the gate-keepers there is one liar and one truth-teller. In fact maybe noone told you that. In fact, maybe there isn't, just as araver says.

Simply "if I was to ask you which gate led to heaven, which would you say?"... or does that allow for the liar to think "neither" and respond anything other than "neither"?

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Darth, "The way to heaven is guarded by a truth teller." Who told you that? It wasn't me. Maybe it was the liar!

Aaryan, noone told the gate-keepers there is one liar and one truth-teller. In fact maybe noone told you that. In fact, maybe there isn't, just as araver says.

Simply "if I was to ask you which gate led to heaven, which would you say?"... or does that allow for the liar to think "neither" and respond anything other than "neither"?

I think,in this case,the liar will lead you to the hell!

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OK, let me try to make it even a more general setting - assume both gatekeepers are either liars or truth-tellers (so they can both be liars, both truth-tellers, or one a liar and one a truth-teller).

Then

Ask anyone of them "If I were to ask you if your gate allows passage to heaven, would you say yes?".

Double negation shows that:

- a truth-teller will answer YES if the gate allows passage to heaven and NO if the gate allows passage to hell

- a liar will always answer YES if the gate allows passage to heaven (to cover up the fact that if you had simply asked him "Does this gate allow passage to heaven", he would have to lie and say NO) and NO if the gate allows passage to hell (again, covering up his answer for the "Does this gate allow passage to heaven" question)

So, regardless of their type: choose that gate if answer is YES, choose the other if answer is NO.

If the liar was standing infront of the gate leading to hell,,,so,,he will say...yes!...what are you going to choose?

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This is probably the most frequently posted puzzle with long discussion and several solutions in

There are a few similar logic problems as well.

For more tips refer to the forum rules.

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