2 Guards Puzzle

[guru]

Traveller Nobby was taken prisoner by the TARTs (Tourist Area Rip-off Touts)

for being unable to pay his padded bill and put in jail.

The jail had 2 gates.

He knew that-

1 gate was guarded by a soldier who always told the truth when asked any question.

The other guard at the other gate always told a lie when asked any question.

Unfortunately little Nobby didn’t know which was which.

But he did know that –

1 gate led to freedom and the other to certain death.

But poor Nobby didn’t know which was which.

But he was told that he could only talk to one of the guards and ask one question before they would both be struck dumb and fall into an eternal sleep.

He could then exit through either one of the gates.

But only one.

We are not sure whether young Nobby escaped.

What question should he have asked?

And which gate should he have gone out of?

[Soju]

He should ask, "does the truthful soldier guard the exit that leads to freedom?" If the answer is "yes", use that exit, if the answer is "no" use the other exit.

[Jimbo551]

I think the question is this -

"If you are the guard who lies, which gate should I leave by?"

The truthful guard will tell him to leave by the wrong gate.

The lying guard will want to tell him to leave by the wrong gate, but as he is being asked to be the truthful guard should tell him to leave by the right gate - but he is the liar so will tell him to leave by the wrong gate.

So, he must leave by the gate opposite to that which either guard tells him.

[Soju]

I think the question is this -

"If you are the guard who lies, which gate should I leave by?"

The truthful guard will tell him to leave by the wrong gate.

The lying guard will want to tell him to leave by the wrong gate, but as he is being asked to be the truthful guard should tell him to leave by the right gate - but he is the liar so will tell him to leave by the wrong gate.

So, he must leave by the gate opposite to that which either guard tells him.

I don't follow you. The truthful guard can't even answer the question, because he's not the guard who lies. Likewise the untruthful guard cannot answer because he is required to lie, but by answering the question, even if the answer regarding the safe gate is a lie, he is telling the truth with respect to being the untruthful guard.

[Medit8]

I think "do you lie?" would suffice as a question to either guard.

[guru]

I think "do you lie?" would suffice as a question to either guard.

But you've now used up your one and only allowed question and both guards fall asleep. Anyway, the liar would also reply with a lie to the qn "do you lie?"

Soju - You must nominate a guard and ask him the one allowed question directly.

[Soju]

I think "do you lie?" would suffice as a question to either guard.

No, that would only ascertain if he was the truthful guard or not. It would give you no information about which exit to use.

Edited to correct that I'm mistaken. It wouldn't tell you anything as both would answer "No".

Edited December 18, 2006 by Soju

[Soju]

Soju - You must nominate a guard and ask him the one allowed question directly.

Yes, just choose either of the guards. It doesn't matter which one you choose. If he answers "yes", use the exit he's guarding but if he answers "no" use the other exit.

[Jimbo551]

I think the question is this -

"If you are the guard who lies, which gate should I leave by?"

The truthful guard will tell him to leave by the wrong gate.

The lying guard will want to tell him to leave by the wrong gate, but as he is being asked to be the truthful guard should tell him to leave by the right gate - but he is the liar so will tell him to leave by the wrong gate.

So, he must leave by the gate opposite to that which either guard tells him.

I don't follow you. The truthful guard can't even answer the question, because he's not the guard who lies. Likewise the untruthful guard cannot answer because he is required to lie, but by answering the question, even if the answer regarding the safe gate is a lie, he is telling the truth with respect to being the untruthful guard.

Ok - then presumably we have to turn this round

"If you are the guard who tells the truth, which gate should I leave by?"

The truthful guard has to tell the truth.

The Lying guard has to tell a lie therefore he has to tell two lies - firstly that he is the truthful guard and secondly which gate to leave by. A double negative which causes him to tell the truth - even inadvertently.

Therefore (and I am dead already as I got it wrong the first time!) leave by the gate they say.

[guru]

He should ask, "does the truthful soldier guard the exit that leads to freedom?" If the answer is "yes", use that exit, if the answer is "no" use the other exit.

No that wouldn't work

[guru]

Ok - then presumably we have to turn this round

"If you are the guard who tells the truth, which gate should I leave by?"

The truthful guard has to tell the truth.

The Lying guard has to tell a lie therefore he has to tell two lies - firstly that he is the truthful guard and secondly which gate to leave by. A double negative which causes him to tell the truth - even inadvertently.

Therefore (and I am dead already as I got it wrong the first time!) leave by the gate they say.

No.

[Soju]

He should ask, "does the truthful soldier guard the exit that leads to freedom?" If the answer is "yes", use that exit, if the answer is "no" use the other exit.

No that wouldn't work

Why not? You have four possibilities...The exit you're at, and ask the question to the guard is...

1. Guarded by the truthful soldier and is the exit to freedom, in which case he answers truthfully "yes" and you go through that gate.

2. Guarded by the truthful soldier and is not the exit to freedom, in which case he answers truthfully "no" and you go through the opposite gate.

3. Guarded by the untruthful soldier and is the exit to freedom, in which case he answers untruthfully "yes" and you go through that gate.

4. Guarded by the untruthful soldier and is not the exit to freedom, in which case he answers untruthfully "no" and you go through the opposite gate.

[guru]

I stand corrected Soju. Your solution does appear to work.

Therefore, there seems to be 2 answers to this.

My solution was

"Which door would the other guard tell me leads to freedom?"

Then proceed out of the opposite door.

[Crossy]

I stand corrected Soju. Your solution does appear to work.

Therefore, there seems to be 2 answers to this.

My solution was

"Which door would the other guard tell me leads to freedom?"

Then proceed out of the opposite door.

Yeah, that's the answer that I was always told. Always more than one solution to any of these logic problems

Hmmm, I'm not sure Soju's answer is correct though, how do I know which door to exit through since there is no indicating of doors?

EDIT Reading it again I suppose it's ok, provided you specify that the guards are stationed by the doors. If they are free to move around only the 'correct' solution works.

The secret is to ask a question that indicates a door and elicits the same answer from both guards.

Edited December 18, 2006 by Crossy

[Soju]

Yeah, that's the answer that I was always told. Always more than one solution to any of these logic problems

Hmmm, I'm not sure Soju's answer is correct though, how do I know which door to exit through since there is no indicating of doors?

EDIT Reading it again I suppose it's ok, provided you specify that the guards are stationed by the doors. If they are free to move around only the 'correct' solution works.

The secret is to ask a question that indicates a door and elicits the same answer from both guards.

The guards being stationed at the gates is not a prerequiste for my solution to work properly. If they're not stationed at the gates, simply reword the question to "Is the truthful guard closer to the exit to freedom than the untruthful guard?" and based on the answer choose the closest or the furthest exit. Or any other question that can somehow correspond a guard to a given exit.

Guru's solution is based on the logical principle that one False plus one True equals a False. You ask a question such that it is "processed" once by the truth/false mechanism of each guard, so that you know the end result is always false and can take the opposite action.

Another solution would be to ask a guard, "if someone asked you which is the exit to freedom, what would your answer be?" Then take the exit he tells you. In this case you are asking to process his answer twice by his truth/false mechanism. So either he lies about his false statement if he's the untruthful guard, or tells the truth about his true statement if he's the truthful guard. In this case, either one False plus one False will equal a True, or one True plus one True will be a True.

Edited December 18, 2006 by Soju

[Crossy]

Another solution would be to ask a guard, "if someone asked you which is the exit to freedom, what would your answer be?" Then take the exit he tells you. In this case you are asking to process his answer twice by his truth/false mechanism. So either he lies about his false statement if he's the untruthful guard, or tells the truth about his true statement if he's the truthful guard. In this case, either one False plus one False will equal a True, or one True plus one True will be a True.

Took a bit of thinking because of the extra process, but yes, I agree with your solution

[rods]

Another solution would be to ask a guard, "if someone asked you which is the exit to freedom, what would your answer be?" Then take the exit he tells you. In this case you are asking to process his answer twice by his truth/false mechanism. So either he lies about his false statement if he's the untruthful guard, or tells the truth about his true statement if he's the truthful guard. In this case, either one False plus one False will equal a True, or one True plus one True will be a True.

Took a bit of thinking because of the extra process, but yes, I agree with your solution

Why can't he just ask one of the guards for a ladder and go over the f***ing wall, eh?