3 doors, three guards, one stone
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You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want to get.
Each door is guarded by a guard:
- Michael, who tells truth with 75% chance;
- Vlad, who lies with 90% chance;
- John, who lies with 70% chance.
You do not know who is who or which door he guards. You may ask each guard 2 questions max but no more than 4 questions in total, because those guys do not like long conversations.
The other thing you have is a magic stone that can be used only once. This stone makes the event with the lowest chance to occur.
You cannot use the stone to do this with multiple events or with an event that has a few independent probabilities. (You cannot ask the 2 guards using the stone). Also, the stone does not count random events.
What is the easiest way which gives you the most chances to go to heaven?
Hint: the solution lies on the surface.
logical-deduction probability liars
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
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$begingroup$
You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want to get.
Each door is guarded by a guard:
- Michael, who tells truth with 75% chance;
- Vlad, who lies with 90% chance;
- John, who lies with 70% chance.
You do not know who is who or which door he guards. You may ask each guard 2 questions max but no more than 4 questions in total, because those guys do not like long conversations.
The other thing you have is a magic stone that can be used only once. This stone makes the event with the lowest chance to occur.
You cannot use the stone to do this with multiple events or with an event that has a few independent probabilities. (You cannot ask the 2 guards using the stone). Also, the stone does not count random events.
What is the easiest way which gives you the most chances to go to heaven?
Hint: the solution lies on the surface.
logical-deduction probability liars
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
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1
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Are only yes/no questions allowed?
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– EKons
Apr 14 at 18:56
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@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
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– Andrii Chumakov
Apr 14 at 18:59
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Michael, who tells truth with 75% chance;-- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?
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– Pod
Apr 15 at 9:38
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Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
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– Overmind
Apr 16 at 7:09
2
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If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
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– cybernard
Apr 16 at 15:14
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show 8 more comments
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You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want to get.
Each door is guarded by a guard:
- Michael, who tells truth with 75% chance;
- Vlad, who lies with 90% chance;
- John, who lies with 70% chance.
You do not know who is who or which door he guards. You may ask each guard 2 questions max but no more than 4 questions in total, because those guys do not like long conversations.
The other thing you have is a magic stone that can be used only once. This stone makes the event with the lowest chance to occur.
You cannot use the stone to do this with multiple events or with an event that has a few independent probabilities. (You cannot ask the 2 guards using the stone). Also, the stone does not count random events.
What is the easiest way which gives you the most chances to go to heaven?
Hint: the solution lies on the surface.
logical-deduction probability liars
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
New contributor
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$endgroup$
You are in a room with three doors. You find out that behind two of these doors, the darkest pit of hell is waiting for you to make a mistake. The other door leads to heaven, where you obviously want to get.
Each door is guarded by a guard:
- Michael, who tells truth with 75% chance;
- Vlad, who lies with 90% chance;
- John, who lies with 70% chance.
You do not know who is who or which door he guards. You may ask each guard 2 questions max but no more than 4 questions in total, because those guys do not like long conversations.
The other thing you have is a magic stone that can be used only once. This stone makes the event with the lowest chance to occur.
You cannot use the stone to do this with multiple events or with an event that has a few independent probabilities. (You cannot ask the 2 guards using the stone). Also, the stone does not count random events.
What is the easiest way which gives you the most chances to go to heaven?
Hint: the solution lies on the surface.
logical-deduction probability liars
logical-deduction probability liars
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
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asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
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edited yesterday
Andrii Chumakov
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
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asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
asked Apr 14 at 16:51
Andrii ChumakovAndrii Chumakov
315212
315212
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Andrii Chumakov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
Andrii Chumakov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Andrii Chumakov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
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Are only yes/no questions allowed?
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– EKons
Apr 14 at 18:56
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@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
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– Andrii Chumakov
Apr 14 at 18:59
5
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Michael, who tells truth with 75% chance;-- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?
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– Pod
Apr 15 at 9:38
2
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Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
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– Overmind
Apr 16 at 7:09
2
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If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
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– cybernard
Apr 16 at 15:14
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show 8 more comments
1
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Are only yes/no questions allowed?
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– EKons
Apr 14 at 18:56
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@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
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– Andrii Chumakov
Apr 14 at 18:59
5
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Michael, who tells truth with 75% chance;-- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?
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– Pod
Apr 15 at 9:38
2
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Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
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– Overmind
Apr 16 at 7:09
2
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If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
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– cybernard
Apr 16 at 15:14
1
1
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Are only yes/no questions allowed?
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– EKons
Apr 14 at 18:56
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Are only yes/no questions allowed?
$endgroup$
– EKons
Apr 14 at 18:56
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@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
$endgroup$
– Andrii Chumakov
Apr 14 at 18:59
$begingroup$
@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
$endgroup$
– Andrii Chumakov
Apr 14 at 18:59
5
5
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Michael, who tells truth with 75% chance; -- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?$endgroup$
– Pod
Apr 15 at 9:38
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Michael, who tells truth with 75% chance; -- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?$endgroup$
– Pod
Apr 15 at 9:38
2
2
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Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
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– Overmind
Apr 16 at 7:09
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Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
$endgroup$
– Overmind
Apr 16 at 7:09
2
2
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If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
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– cybernard
Apr 16 at 15:14
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If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
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– cybernard
Apr 16 at 15:14
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show 8 more comments
11 Answers
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No questions are required!
Use the magic stone, then try one of the doors. It's less likely to get the right door (1/3) than one of the wrong ones (2/3), so you'll end up in the right place
answered Apr 14 at 20:33
StephenTGStephenTG
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With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
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– Chen Li Yong
Apr 15 at 4:23
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Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
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– Andrii Chumakov
Apr 15 at 5:33
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I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
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– Annosz
Apr 15 at 10:20
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But the door is either to heaven or to hell. This isn't a probabilistic thing.
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– Acccumulation
Apr 15 at 17:24
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@Accumulation But your choice of the door is a probabilistic thing.
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– Ross Presser
Apr 15 at 20:01
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I will ask using the stone: "what door would you tell me that will take me to heaven if I ask you using the stone?". The answer is always the correct door.
For clarify:
If I ask with the stone to Michael, he will be lying. If I ask him (with the stone) "what door will take me to heaven", he will say one of the hell's doors, but I ask about this question (with the stone), so he have to lie and say the heaven's door, because is the only answer that can't be truth.
Obviously, Vlad and John will say the truth, so they will say the heaven´s door.
No matter who you ask, he will answer the correct door.
answered Apr 15 at 16:48
HermesHermes
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You do not know who is who, that's the main problem. Nice try.
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– Andrii Chumakov
Apr 16 at 18:17
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@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
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– Vincent
2 days ago
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The stone can be used only once. You can't ask all three guards with it.
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– Daniel P
2 days ago
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I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
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– Hermes
2 days ago
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Ask the following question of all three guards:
If I asked you which door you were guarding, would you say it was the door to heaven?
Now the number of Yeses (Y) will be between 0 and 3 inclusive.
If Y=1, go through that door. The position may either be
1.
(Michael, John, Vlad) = (Yes, No, No)
in which case you go to heaven, or it may be one of
(No, Yes, No) and(No, No, Yes)
in which case you go to hell.
If Y=2, namely
3.
(Yes, Yes, No), (Yes, No, Yes), or (No, Yes, Yes).
then pick one of the Yeses at random and ask the utterer the same question again. If he changes to a No,
go through the door which had the other Yes.
If he doesn't,
pick one of the Yes doors at random and go through it.
If Y=3, namely
(Yes, Yes, Yes)
then again, pick one of the Yeses at random and ask the utterer the same question again.
The number of remaining Yeses will be two or three. Pick one of them at random and go through the corresponding door.
The last possibility is that Y=0:
5.
(No, No, No)
Oh dear.
Pick a guard at random and repeat the question. The number of Yeses will now be one or zero. If it is one, go through the corresponding door. If it is zero, pick one of three doors at random and hope for the best.
This is ignoring the magic stone. I think StephenTG got the right answer. This was basically a trick question. But if you ignore the magic stone, the resulting question is still a good puzzle, and the above may be the best strategy.
Edit
I've edited this in light of Amorydai's helpful comment.
For the three equiprobable cases of which door leads to heaven, the probabilities of each guard saying "Yes" are as follows (writing M, J, V for Michael, John, Vlad):
Case 1: M's door leads to heaven
M: $0.75^2 + 0.25^2 = 0.625$;
J: $2 * 0.7*0.3 = 0.42$
V: $2 * 0.9*0.1 = 0.18$
Case 2: J's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $0.7^2 * 0.3^2 = 0.58$
V: $2 * 0.9*0.1 = 0.18$
Case 3: V's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $2 * 0.7*0.3 = 0.42$
V: $0.9^2 + 0.1^2 = 0.82$
In each case, the number of possible sets of answers to the first 3 questions is 8, of which 5 have $Ynot=1$ and therefore require a 4th question. I haven't yet worked out the probability of going to heaven if you use my suggested strategy, but I assert that it is greater than 1/3.
We can start the calculation as follows.
Case 1
YNN has probability $0.625*0.58*0.82= 0.29725$.
YYN has probability $0.625*0.42*0.82= 0.21525$.
The probability that we choose the 2nd guard to put our 4th question to is 1/2, and then the probability of his saying N is 0.58 (heaven) and Y (0.42) (half chance of heaven); and the probability of our choosing the 1st guard is also 1/2, upon which the probability of his saying Y is 0.75 (half chance of heaven) and N (hell) is 0.25.
So given YYN our chance of getting to heaven is $0.21525 * big(0.5*(0.58 +0.5*0.42)+(0.5*0.75)big)=0.125383125$.
So already, having considered only YYN and YNN, we know that our probability of reaching heaven in Case 1 (door to heaven is guarded by Michael) is at least $0.21525+0.125383125=0.340633125$.
Since this is greater than 1/3, we have proved that in Case 1 the strategy is better than picking a door completely at random and I believe that that is also so in each of Cases 2 and 3 :-)
answered Apr 15 at 2:02
h34h34
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I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
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– Amorydai
Apr 15 at 4:55
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That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
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– Amorydai
Apr 15 at 5:12
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Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
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– h34
Apr 15 at 10:08
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I'd go with this:
Go to any guard, use the magic stone, and ask the question:
Which of the remaining two guards has a greater chance of lying than speaking the truth?
Special thanks to @Amorydai for their valuable feedback in comments
If it is Michel
Since he will lie, so he'll say
"None"
If it is Vlad
He will point to one guard, who will be John, so the other would be Michel
If it is John
He will point to one guard, who will be Vlad, so the other would be Michel
So
I'll identify Michel who will say the truth 75% of times, and ask him the second question
"Which door leads to heaven"
It is a 75% chance that he'll tell the truth
answered Apr 14 at 20:06
EagleEagle
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Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
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– Amorydai
Apr 14 at 22:37
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@Amorydai The guards know is who. See OP's comment here
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– Eagle
2 days ago
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He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
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– Hermes
2 days ago
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@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
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– Amorydai
2 days ago
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@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
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– Eagle
2 days ago
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What about
Asking them all at once with the stone?
Since the lowest occurrence chance event will happen. Just ask all of them which way is to heaven and two of them will point to one same door.
answered Apr 15 at 9:09
MichaelMichael
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Nice try. Sorry, but the stone can be only used to make one event happen
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– Andrii Chumakov
Apr 15 at 17:24
add a comment |
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The real question is:
How do you know that 1 of the doors leads to heaven and the other 2 lead to hell? If you learn that from the guards, that means that the correct door is most likely Vlads door, because he has the highest chance of lying and his door supposedly leads to hell.
Further more:
The text for the stone states the "stone makes the event with the lowest chance to occur". Excluding random events we could come up with, the event with the lowest chance to occur would be Vlad telling the truth.
Thus:
You would use the stone and ask him "Does this door lead to hell." His answer should be "No".
Also:
It fits with the 4 question rule. The first 3 questions are you asking each guard what their name is, Vlad should lie to you that he is John and the final question is the one directed at Vlad with the stone.
answered Apr 15 at 23:45
Бранко РБранко Р
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Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
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– Andrii Chumakov
Apr 16 at 15:11
add a comment |
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You just need one question and u have to use the stone.
Ask the most left guard:
"What would the middle guard answer, if I would ask him:
What would the right guard answer, if I would ask him what's the door to hell"
(crazy question but I needed to include all 3 guards in one question)
With the stone, the event with the lowest chance would be that 2 guards will tell the truth and one will lie. -> The asked guard will lie -> He points on the door to heaven! -> 100% chance to go to heaven!
edited Apr 16 at 17:50
Rubio♦
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
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Just ask the room
"Which is the door to heaven?" while using the stone. The least likely outcome is that Vlad will answer you truthfully, so whoever answers you is Vlad, and he's telling you the correct door.
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
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Well, the post by StephenTG is correct without asking questions.
Following the hint, here's my answer for if you HAVE to ask a question.
Because Vlad LIES 90% of the time, then he's truthful 10% of the time. Therefore, by using the stone to make that 10% happen, Vlad tells the truth of which door to go through.
answered yesterday
CStafford-14CStafford-14
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That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
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– Andrii Chumakov
yesterday
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Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
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– CStafford-14
yesterday
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Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
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– CStafford-14
yesterday
1
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John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
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– Andrii Chumakov
yesterday
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As long as I don't ask Michael, I'm fine.
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– CStafford-14
yesterday
add a comment |
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If, contrary to StephenTG's answer, we interpret the stone as only applying to random events, then we can simply ask
Which of these doors leads to hell?
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
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You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
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– Armin
Apr 16 at 11:43
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Am I confused...It seems like asking Vlad with the stone is the best option because is has a 10% chance of telling the truth. "This stone makes the event with the lowest chance to occur". So Then Vlad tells the truth, and you leave asking only 1 question?
Then just ask Michael a couple of times for fun because you already know the truth.
Michael should agree with Vlad at least once if not more.
answered Apr 15 at 20:13
cybernardcybernard
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How do you know who is Vlad and who is not?
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– Eagle
Apr 15 at 20:16
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@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
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– cybernard
Apr 15 at 20:18
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Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
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– Eagle
Apr 15 at 20:19
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@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
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– Armin
Apr 16 at 11:42
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
|
show 2 more comments
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11 Answers
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11 Answers
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active
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$begingroup$
No questions are required!
Use the magic stone, then try one of the doors. It's less likely to get the right door (1/3) than one of the wrong ones (2/3), so you'll end up in the right place
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
$endgroup$
16
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
3
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
10
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
5
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
3
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
|
show 10 more comments
$begingroup$
No questions are required!
Use the magic stone, then try one of the doors. It's less likely to get the right door (1/3) than one of the wrong ones (2/3), so you'll end up in the right place
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
$endgroup$
16
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
3
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
10
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
5
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
3
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
|
show 10 more comments
$begingroup$
No questions are required!
Use the magic stone, then try one of the doors. It's less likely to get the right door (1/3) than one of the wrong ones (2/3), so you'll end up in the right place
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
$endgroup$
No questions are required!
Use the magic stone, then try one of the doors. It's less likely to get the right door (1/3) than one of the wrong ones (2/3), so you'll end up in the right place
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
answered Apr 14 at 20:33
StephenTGStephenTG
2,03711122
2,03711122
16
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
3
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
10
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
5
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
3
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
|
show 10 more comments
16
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
3
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
10
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
5
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
3
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
16
16
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
$begingroup$
With this answer, I now feel like the puzzle was somehow like a troll puzzle, that tries to distract you from the actual answer. :D
$endgroup$
– Chen Li Yong
Apr 15 at 4:23
3
3
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
$begingroup$
Yes, that's the simplest solution, to this problem. The problem is much easier than it seems to be.
$endgroup$
– Andrii Chumakov
Apr 15 at 5:33
10
10
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
$begingroup$
I was thinking about this, but I always tought that "yes, but the least likely situation is that you get hit by a bus or turn into a racoon or something else" :D
$endgroup$
– Annosz
Apr 15 at 10:20
5
5
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
$begingroup$
But the door is either to heaven or to hell. This isn't a probabilistic thing.
$endgroup$
– Acccumulation
Apr 15 at 17:24
3
3
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
$begingroup$
@Accumulation But your choice of the door is a probabilistic thing.
$endgroup$
– Ross Presser
Apr 15 at 20:01
|
show 10 more comments
$begingroup$
I will ask using the stone: "what door would you tell me that will take me to heaven if I ask you using the stone?". The answer is always the correct door.
For clarify:
If I ask with the stone to Michael, he will be lying. If I ask him (with the stone) "what door will take me to heaven", he will say one of the hell's doors, but I ask about this question (with the stone), so he have to lie and say the heaven's door, because is the only answer that can't be truth.
Obviously, Vlad and John will say the truth, so they will say the heaven´s door.
No matter who you ask, he will answer the correct door.
answered Apr 15 at 16:48
HermesHermes
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
5
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
add a comment |
$begingroup$
I will ask using the stone: "what door would you tell me that will take me to heaven if I ask you using the stone?". The answer is always the correct door.
For clarify:
If I ask with the stone to Michael, he will be lying. If I ask him (with the stone) "what door will take me to heaven", he will say one of the hell's doors, but I ask about this question (with the stone), so he have to lie and say the heaven's door, because is the only answer that can't be truth.
Obviously, Vlad and John will say the truth, so they will say the heaven´s door.
No matter who you ask, he will answer the correct door.
answered Apr 15 at 16:48
HermesHermes
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
5
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
add a comment |
$begingroup$
I will ask using the stone: "what door would you tell me that will take me to heaven if I ask you using the stone?". The answer is always the correct door.
For clarify:
If I ask with the stone to Michael, he will be lying. If I ask him (with the stone) "what door will take me to heaven", he will say one of the hell's doors, but I ask about this question (with the stone), so he have to lie and say the heaven's door, because is the only answer that can't be truth.
Obviously, Vlad and John will say the truth, so they will say the heaven´s door.
No matter who you ask, he will answer the correct door.
answered Apr 15 at 16:48
HermesHermes
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I will ask using the stone: "what door would you tell me that will take me to heaven if I ask you using the stone?". The answer is always the correct door.
For clarify:
If I ask with the stone to Michael, he will be lying. If I ask him (with the stone) "what door will take me to heaven", he will say one of the hell's doors, but I ask about this question (with the stone), so he have to lie and say the heaven's door, because is the only answer that can't be truth.
Obviously, Vlad and John will say the truth, so they will say the heaven´s door.
No matter who you ask, he will answer the correct door.
answered Apr 15 at 16:48
HermesHermes
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
answered Apr 15 at 16:48
HermesHermes
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 15 at 16:48
HermesHermes
3414
answered Apr 15 at 16:48
HermesHermes
3414
3414
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Hermes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
5
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
add a comment |
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
5
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
$begingroup$
You do not know who is who, that's the main problem. Nice try.
$endgroup$
– Andrii Chumakov
Apr 16 at 18:17
5
5
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
@Andrii If I understand Hermes' answer correctly all three will give the same answer, so it doesn't really matter who is who
$endgroup$
– Vincent
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
The stone can be used only once. You can't ask all three guards with it.
$endgroup$
– Daniel P
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
$begingroup$
I'm not asking all three: only one, at random. Whoever he is, the answer will be the same.
$endgroup$
– Hermes
2 days ago
add a comment |
$begingroup$
Ask the following question of all three guards:
If I asked you which door you were guarding, would you say it was the door to heaven?
Now the number of Yeses (Y) will be between 0 and 3 inclusive.
If Y=1, go through that door. The position may either be
1.
(Michael, John, Vlad) = (Yes, No, No)
in which case you go to heaven, or it may be one of
(No, Yes, No) and(No, No, Yes)
in which case you go to hell.
If Y=2, namely
3.
(Yes, Yes, No), (Yes, No, Yes), or (No, Yes, Yes).
then pick one of the Yeses at random and ask the utterer the same question again. If he changes to a No,
go through the door which had the other Yes.
If he doesn't,
pick one of the Yes doors at random and go through it.
If Y=3, namely
(Yes, Yes, Yes)
then again, pick one of the Yeses at random and ask the utterer the same question again.
The number of remaining Yeses will be two or three. Pick one of them at random and go through the corresponding door.
The last possibility is that Y=0:
5.
(No, No, No)
Oh dear.
Pick a guard at random and repeat the question. The number of Yeses will now be one or zero. If it is one, go through the corresponding door. If it is zero, pick one of three doors at random and hope for the best.
This is ignoring the magic stone. I think StephenTG got the right answer. This was basically a trick question. But if you ignore the magic stone, the resulting question is still a good puzzle, and the above may be the best strategy.
Edit
I've edited this in light of Amorydai's helpful comment.
For the three equiprobable cases of which door leads to heaven, the probabilities of each guard saying "Yes" are as follows (writing M, J, V for Michael, John, Vlad):
Case 1: M's door leads to heaven
M: $0.75^2 + 0.25^2 = 0.625$;
J: $2 * 0.7*0.3 = 0.42$
V: $2 * 0.9*0.1 = 0.18$
Case 2: J's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $0.7^2 * 0.3^2 = 0.58$
V: $2 * 0.9*0.1 = 0.18$
Case 3: V's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $2 * 0.7*0.3 = 0.42$
V: $0.9^2 + 0.1^2 = 0.82$
In each case, the number of possible sets of answers to the first 3 questions is 8, of which 5 have $Ynot=1$ and therefore require a 4th question. I haven't yet worked out the probability of going to heaven if you use my suggested strategy, but I assert that it is greater than 1/3.
We can start the calculation as follows.
Case 1
YNN has probability $0.625*0.58*0.82= 0.29725$.
YYN has probability $0.625*0.42*0.82= 0.21525$.
The probability that we choose the 2nd guard to put our 4th question to is 1/2, and then the probability of his saying N is 0.58 (heaven) and Y (0.42) (half chance of heaven); and the probability of our choosing the 1st guard is also 1/2, upon which the probability of his saying Y is 0.75 (half chance of heaven) and N (hell) is 0.25.
So given YYN our chance of getting to heaven is $0.21525 * big(0.5*(0.58 +0.5*0.42)+(0.5*0.75)big)=0.125383125$.
So already, having considered only YYN and YNN, we know that our probability of reaching heaven in Case 1 (door to heaven is guarded by Michael) is at least $0.21525+0.125383125=0.340633125$.
Since this is greater than 1/3, we have proved that in Case 1 the strategy is better than picking a door completely at random and I believe that that is also so in each of Cases 2 and 3 :-)
answered Apr 15 at 2:02
h34h34
3,72311141
$endgroup$
1
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
1
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
add a comment |
$begingroup$
Ask the following question of all three guards:
If I asked you which door you were guarding, would you say it was the door to heaven?
Now the number of Yeses (Y) will be between 0 and 3 inclusive.
If Y=1, go through that door. The position may either be
1.
(Michael, John, Vlad) = (Yes, No, No)
in which case you go to heaven, or it may be one of
(No, Yes, No) and(No, No, Yes)
in which case you go to hell.
If Y=2, namely
3.
(Yes, Yes, No), (Yes, No, Yes), or (No, Yes, Yes).
then pick one of the Yeses at random and ask the utterer the same question again. If he changes to a No,
go through the door which had the other Yes.
If he doesn't,
pick one of the Yes doors at random and go through it.
If Y=3, namely
(Yes, Yes, Yes)
then again, pick one of the Yeses at random and ask the utterer the same question again.
The number of remaining Yeses will be two or three. Pick one of them at random and go through the corresponding door.
The last possibility is that Y=0:
5.
(No, No, No)
Oh dear.
Pick a guard at random and repeat the question. The number of Yeses will now be one or zero. If it is one, go through the corresponding door. If it is zero, pick one of three doors at random and hope for the best.
This is ignoring the magic stone. I think StephenTG got the right answer. This was basically a trick question. But if you ignore the magic stone, the resulting question is still a good puzzle, and the above may be the best strategy.
Edit
I've edited this in light of Amorydai's helpful comment.
For the three equiprobable cases of which door leads to heaven, the probabilities of each guard saying "Yes" are as follows (writing M, J, V for Michael, John, Vlad):
Case 1: M's door leads to heaven
M: $0.75^2 + 0.25^2 = 0.625$;
J: $2 * 0.7*0.3 = 0.42$
V: $2 * 0.9*0.1 = 0.18$
Case 2: J's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $0.7^2 * 0.3^2 = 0.58$
V: $2 * 0.9*0.1 = 0.18$
Case 3: V's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $2 * 0.7*0.3 = 0.42$
V: $0.9^2 + 0.1^2 = 0.82$
In each case, the number of possible sets of answers to the first 3 questions is 8, of which 5 have $Ynot=1$ and therefore require a 4th question. I haven't yet worked out the probability of going to heaven if you use my suggested strategy, but I assert that it is greater than 1/3.
We can start the calculation as follows.
Case 1
YNN has probability $0.625*0.58*0.82= 0.29725$.
YYN has probability $0.625*0.42*0.82= 0.21525$.
The probability that we choose the 2nd guard to put our 4th question to is 1/2, and then the probability of his saying N is 0.58 (heaven) and Y (0.42) (half chance of heaven); and the probability of our choosing the 1st guard is also 1/2, upon which the probability of his saying Y is 0.75 (half chance of heaven) and N (hell) is 0.25.
So given YYN our chance of getting to heaven is $0.21525 * big(0.5*(0.58 +0.5*0.42)+(0.5*0.75)big)=0.125383125$.
So already, having considered only YYN and YNN, we know that our probability of reaching heaven in Case 1 (door to heaven is guarded by Michael) is at least $0.21525+0.125383125=0.340633125$.
Since this is greater than 1/3, we have proved that in Case 1 the strategy is better than picking a door completely at random and I believe that that is also so in each of Cases 2 and 3 :-)
answered Apr 15 at 2:02
h34h34
3,72311141
$endgroup$
1
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
1
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
add a comment |
$begingroup$
Ask the following question of all three guards:
If I asked you which door you were guarding, would you say it was the door to heaven?
Now the number of Yeses (Y) will be between 0 and 3 inclusive.
If Y=1, go through that door. The position may either be
1.
(Michael, John, Vlad) = (Yes, No, No)
in which case you go to heaven, or it may be one of
(No, Yes, No) and(No, No, Yes)
in which case you go to hell.
If Y=2, namely
3.
(Yes, Yes, No), (Yes, No, Yes), or (No, Yes, Yes).
then pick one of the Yeses at random and ask the utterer the same question again. If he changes to a No,
go through the door which had the other Yes.
If he doesn't,
pick one of the Yes doors at random and go through it.
If Y=3, namely
(Yes, Yes, Yes)
then again, pick one of the Yeses at random and ask the utterer the same question again.
The number of remaining Yeses will be two or three. Pick one of them at random and go through the corresponding door.
The last possibility is that Y=0:
5.
(No, No, No)
Oh dear.
Pick a guard at random and repeat the question. The number of Yeses will now be one or zero. If it is one, go through the corresponding door. If it is zero, pick one of three doors at random and hope for the best.
This is ignoring the magic stone. I think StephenTG got the right answer. This was basically a trick question. But if you ignore the magic stone, the resulting question is still a good puzzle, and the above may be the best strategy.
Edit
I've edited this in light of Amorydai's helpful comment.
For the three equiprobable cases of which door leads to heaven, the probabilities of each guard saying "Yes" are as follows (writing M, J, V for Michael, John, Vlad):
Case 1: M's door leads to heaven
M: $0.75^2 + 0.25^2 = 0.625$;
J: $2 * 0.7*0.3 = 0.42$
V: $2 * 0.9*0.1 = 0.18$
Case 2: J's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $0.7^2 * 0.3^2 = 0.58$
V: $2 * 0.9*0.1 = 0.18$
Case 3: V's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $2 * 0.7*0.3 = 0.42$
V: $0.9^2 + 0.1^2 = 0.82$
In each case, the number of possible sets of answers to the first 3 questions is 8, of which 5 have $Ynot=1$ and therefore require a 4th question. I haven't yet worked out the probability of going to heaven if you use my suggested strategy, but I assert that it is greater than 1/3.
We can start the calculation as follows.
Case 1
YNN has probability $0.625*0.58*0.82= 0.29725$.
YYN has probability $0.625*0.42*0.82= 0.21525$.
The probability that we choose the 2nd guard to put our 4th question to is 1/2, and then the probability of his saying N is 0.58 (heaven) and Y (0.42) (half chance of heaven); and the probability of our choosing the 1st guard is also 1/2, upon which the probability of his saying Y is 0.75 (half chance of heaven) and N (hell) is 0.25.
So given YYN our chance of getting to heaven is $0.21525 * big(0.5*(0.58 +0.5*0.42)+(0.5*0.75)big)=0.125383125$.
So already, having considered only YYN and YNN, we know that our probability of reaching heaven in Case 1 (door to heaven is guarded by Michael) is at least $0.21525+0.125383125=0.340633125$.
Since this is greater than 1/3, we have proved that in Case 1 the strategy is better than picking a door completely at random and I believe that that is also so in each of Cases 2 and 3 :-)
answered Apr 15 at 2:02
h34h34
3,72311141
$endgroup$
Ask the following question of all three guards:
If I asked you which door you were guarding, would you say it was the door to heaven?
Now the number of Yeses (Y) will be between 0 and 3 inclusive.
If Y=1, go through that door. The position may either be
1.
(Michael, John, Vlad) = (Yes, No, No)
in which case you go to heaven, or it may be one of
(No, Yes, No) and(No, No, Yes)
in which case you go to hell.
If Y=2, namely
3.
(Yes, Yes, No), (Yes, No, Yes), or (No, Yes, Yes).
then pick one of the Yeses at random and ask the utterer the same question again. If he changes to a No,
go through the door which had the other Yes.
If he doesn't,
pick one of the Yes doors at random and go through it.
If Y=3, namely
(Yes, Yes, Yes)
then again, pick one of the Yeses at random and ask the utterer the same question again.
The number of remaining Yeses will be two or three. Pick one of them at random and go through the corresponding door.
The last possibility is that Y=0:
5.
(No, No, No)
Oh dear.
Pick a guard at random and repeat the question. The number of Yeses will now be one or zero. If it is one, go through the corresponding door. If it is zero, pick one of three doors at random and hope for the best.
This is ignoring the magic stone. I think StephenTG got the right answer. This was basically a trick question. But if you ignore the magic stone, the resulting question is still a good puzzle, and the above may be the best strategy.
Edit
I've edited this in light of Amorydai's helpful comment.
For the three equiprobable cases of which door leads to heaven, the probabilities of each guard saying "Yes" are as follows (writing M, J, V for Michael, John, Vlad):
Case 1: M's door leads to heaven
M: $0.75^2 + 0.25^2 = 0.625$;
J: $2 * 0.7*0.3 = 0.42$
V: $2 * 0.9*0.1 = 0.18$
Case 2: J's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $0.7^2 * 0.3^2 = 0.58$
V: $2 * 0.9*0.1 = 0.18$
Case 3: V's door leads to heaven
M: $2 * 0.75 * 0.25 = 0.375$;
J: $2 * 0.7*0.3 = 0.42$
V: $0.9^2 + 0.1^2 = 0.82$
In each case, the number of possible sets of answers to the first 3 questions is 8, of which 5 have $Ynot=1$ and therefore require a 4th question. I haven't yet worked out the probability of going to heaven if you use my suggested strategy, but I assert that it is greater than 1/3.
We can start the calculation as follows.
Case 1
YNN has probability $0.625*0.58*0.82= 0.29725$.
YYN has probability $0.625*0.42*0.82= 0.21525$.
The probability that we choose the 2nd guard to put our 4th question to is 1/2, and then the probability of his saying N is 0.58 (heaven) and Y (0.42) (half chance of heaven); and the probability of our choosing the 1st guard is also 1/2, upon which the probability of his saying Y is 0.75 (half chance of heaven) and N (hell) is 0.25.
So given YYN our chance of getting to heaven is $0.21525 * big(0.5*(0.58 +0.5*0.42)+(0.5*0.75)big)=0.125383125$.
So already, having considered only YYN and YNN, we know that our probability of reaching heaven in Case 1 (door to heaven is guarded by Michael) is at least $0.21525+0.125383125=0.340633125$.
Since this is greater than 1/3, we have proved that in Case 1 the strategy is better than picking a door completely at random and I believe that that is also so in each of Cases 2 and 3 :-)
answered Apr 15 at 2:02
h34h34
3,72311141
edited Apr 15 at 13:18
answered Apr 15 at 2:02
h34h34
3,72311141
answered Apr 15 at 2:02
h34h34
3,72311141
answered Apr 15 at 2:02
h34h34
3,72311141
3,72311141
1
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
1
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
add a comment |
1
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
1
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
1
1
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
$begingroup$
I’m a bit confused on how you calculated the probabilities. The question you ask will lead to a yes if the guard tells the truth both times or lies both times (assuming the guard is actually guarding the door to heaven). So I understand Michael’s percentage. For John and Vlad it should really be the same, so .7*.7+.3*.3 for John and .9*.9+.1*.1 for Vlad. These are all over 50% so the most likely response would be 3 yeses.
$endgroup$
– Amorydai
Apr 15 at 4:55
1
1
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
That’s if we assume they’re guarding the door to heaven, if they are not, then that would be the percent chance of them saying no. Since they each have a 1/3 chance of actually guarding the door to heaven and 2/3 chance of guarding the door to hell, the chances of them answering yes to that question are actually all below 50%
$endgroup$
– Amorydai
Apr 15 at 5:12
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
$begingroup$
Hmm yes, thanks. You're right. So running through them, for Yeses we get: (Michael) 1/3 * (0.75^2 + 0.25^2) + 2/3 * (0.75*0.25 + 0.25*0.75) = 0.458333; (John) 1/3 * (0.7 ^2 +0.3*^2) + 2/3 * (0.7*0.3 + 0.3*0.7) = 0.473333; (Vlad) 1/3 * (0.9^2 +0.1*^2) + 2/3 * (0.9*0.1+ 0.1*0.9) = 0.393333. Now I am confused. If we ignore the stone what would be the best strategy?
$endgroup$
– h34
Apr 15 at 10:08
add a comment |
$begingroup$
I'd go with this:
Go to any guard, use the magic stone, and ask the question:
Which of the remaining two guards has a greater chance of lying than speaking the truth?
Special thanks to @Amorydai for their valuable feedback in comments
If it is Michel
Since he will lie, so he'll say
"None"
If it is Vlad
He will point to one guard, who will be John, so the other would be Michel
If it is John
He will point to one guard, who will be Vlad, so the other would be Michel
So
I'll identify Michel who will say the truth 75% of times, and ask him the second question
"Which door leads to heaven"
It is a 75% chance that he'll tell the truth
answered Apr 14 at 20:06
EagleEagle
720226
$endgroup$
8
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
|
show 2 more comments
$begingroup$
I'd go with this:
Go to any guard, use the magic stone, and ask the question:
Which of the remaining two guards has a greater chance of lying than speaking the truth?
Special thanks to @Amorydai for their valuable feedback in comments
If it is Michel
Since he will lie, so he'll say
"None"
If it is Vlad
He will point to one guard, who will be John, so the other would be Michel
If it is John
He will point to one guard, who will be Vlad, so the other would be Michel
So
I'll identify Michel who will say the truth 75% of times, and ask him the second question
"Which door leads to heaven"
It is a 75% chance that he'll tell the truth
answered Apr 14 at 20:06
EagleEagle
720226
$endgroup$
8
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
|
show 2 more comments
$begingroup$
I'd go with this:
Go to any guard, use the magic stone, and ask the question:
Which of the remaining two guards has a greater chance of lying than speaking the truth?
Special thanks to @Amorydai for their valuable feedback in comments
If it is Michel
Since he will lie, so he'll say
"None"
If it is Vlad
He will point to one guard, who will be John, so the other would be Michel
If it is John
He will point to one guard, who will be Vlad, so the other would be Michel
So
I'll identify Michel who will say the truth 75% of times, and ask him the second question
"Which door leads to heaven"
It is a 75% chance that he'll tell the truth
answered Apr 14 at 20:06
EagleEagle
720226
$endgroup$
I'd go with this:
Go to any guard, use the magic stone, and ask the question:
Which of the remaining two guards has a greater chance of lying than speaking the truth?
Special thanks to @Amorydai for their valuable feedback in comments
If it is Michel
Since he will lie, so he'll say
"None"
If it is Vlad
He will point to one guard, who will be John, so the other would be Michel
If it is John
He will point to one guard, who will be Vlad, so the other would be Michel
So
I'll identify Michel who will say the truth 75% of times, and ask him the second question
"Which door leads to heaven"
It is a 75% chance that he'll tell the truth
answered Apr 14 at 20:06
EagleEagle
720226
edited yesterday
answered Apr 14 at 20:06
EagleEagle
720226
answered Apr 14 at 20:06
EagleEagle
720226
answered Apr 14 at 20:06
EagleEagle
720226
720226
8
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
|
show 2 more comments
8
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
8
8
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
Not quite. Without the magic stone all the guards a basically random. If you ask one of them “which guard will lie”, they will not have an answer for you. It’s impossible to tell when someone will lie or tell the truth. That’s like asking “when will the next die roll land on a 3”. Whether the guard is lying or telling the truth, he will not know the answer to that.
$endgroup$
– Amorydai
Apr 14 at 22:37
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
@Amorydai The guards know is who. See OP's comment here
$endgroup$
– Eagle
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
He is using the stone for that question, which allows him to locate Michael. Then he asks the one who now he knows that is Michael (without the stone), which gives him a 75% chance. He can even increase the chances by asking the other two questions to Vlad and John, knowing that in both cases they probably lie.
$endgroup$
– Hermes
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Akari It doesn’t matter if the guards know who is who. I know when I roll a die it will land on an even number half the time. And I always tell the truth. If someone asks me “on your next die roll will it be an even number?”. Should I say yes or no? I tell the truth, I don’t predict the future. None of the guards will know who will lie next, so the question cannot be answered.
$endgroup$
– Amorydai
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
$begingroup$
@Amorydai oh okay. Now I understood what you meant. Thanks! I've modified my answer.
$endgroup$
– Eagle
2 days ago
|
show 2 more comments
$begingroup$
What about
Asking them all at once with the stone?
Since the lowest occurrence chance event will happen. Just ask all of them which way is to heaven and two of them will point to one same door.
answered Apr 15 at 9:09
MichaelMichael
311
New contributor
Michael is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
add a comment |
$begingroup$
What about
Asking them all at once with the stone?
Since the lowest occurrence chance event will happen. Just ask all of them which way is to heaven and two of them will point to one same door.
answered Apr 15 at 9:09
MichaelMichael
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1
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Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
add a comment |
$begingroup$
What about
Asking them all at once with the stone?
Since the lowest occurrence chance event will happen. Just ask all of them which way is to heaven and two of them will point to one same door.
answered Apr 15 at 9:09
MichaelMichael
311
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$endgroup$
What about
Asking them all at once with the stone?
Since the lowest occurrence chance event will happen. Just ask all of them which way is to heaven and two of them will point to one same door.
answered Apr 15 at 9:09
MichaelMichael
311
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answered Apr 15 at 9:09
MichaelMichael
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answered Apr 15 at 9:09
MichaelMichael
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answered Apr 15 at 9:09
MichaelMichael
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1
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Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
add a comment |
1
$begingroup$
Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
1
1
$begingroup$
Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
$begingroup$
Nice try. Sorry, but the stone can be only used to make one event happen
$endgroup$
– Andrii Chumakov
Apr 15 at 17:24
add a comment |
$begingroup$
The real question is:
How do you know that 1 of the doors leads to heaven and the other 2 lead to hell? If you learn that from the guards, that means that the correct door is most likely Vlads door, because he has the highest chance of lying and his door supposedly leads to hell.
Further more:
The text for the stone states the "stone makes the event with the lowest chance to occur". Excluding random events we could come up with, the event with the lowest chance to occur would be Vlad telling the truth.
Thus:
You would use the stone and ask him "Does this door lead to hell." His answer should be "No".
Also:
It fits with the 4 question rule. The first 3 questions are you asking each guard what their name is, Vlad should lie to you that he is John and the final question is the one directed at Vlad with the stone.
answered Apr 15 at 23:45
Бранко РБранко Р
312
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Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
add a comment |
$begingroup$
The real question is:
How do you know that 1 of the doors leads to heaven and the other 2 lead to hell? If you learn that from the guards, that means that the correct door is most likely Vlads door, because he has the highest chance of lying and his door supposedly leads to hell.
Further more:
The text for the stone states the "stone makes the event with the lowest chance to occur". Excluding random events we could come up with, the event with the lowest chance to occur would be Vlad telling the truth.
Thus:
You would use the stone and ask him "Does this door lead to hell." His answer should be "No".
Also:
It fits with the 4 question rule. The first 3 questions are you asking each guard what their name is, Vlad should lie to you that he is John and the final question is the one directed at Vlad with the stone.
answered Apr 15 at 23:45
Бранко РБранко Р
312
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Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
add a comment |
$begingroup$
The real question is:
How do you know that 1 of the doors leads to heaven and the other 2 lead to hell? If you learn that from the guards, that means that the correct door is most likely Vlads door, because he has the highest chance of lying and his door supposedly leads to hell.
Further more:
The text for the stone states the "stone makes the event with the lowest chance to occur". Excluding random events we could come up with, the event with the lowest chance to occur would be Vlad telling the truth.
Thus:
You would use the stone and ask him "Does this door lead to hell." His answer should be "No".
Also:
It fits with the 4 question rule. The first 3 questions are you asking each guard what their name is, Vlad should lie to you that he is John and the final question is the one directed at Vlad with the stone.
answered Apr 15 at 23:45
Бранко РБранко Р
312
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$endgroup$
The real question is:
How do you know that 1 of the doors leads to heaven and the other 2 lead to hell? If you learn that from the guards, that means that the correct door is most likely Vlads door, because he has the highest chance of lying and his door supposedly leads to hell.
Further more:
The text for the stone states the "stone makes the event with the lowest chance to occur". Excluding random events we could come up with, the event with the lowest chance to occur would be Vlad telling the truth.
Thus:
You would use the stone and ask him "Does this door lead to hell." His answer should be "No".
Also:
It fits with the 4 question rule. The first 3 questions are you asking each guard what their name is, Vlad should lie to you that he is John and the final question is the one directed at Vlad with the stone.
answered Apr 15 at 23:45
Бранко РБранко Р
312
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answered Apr 15 at 23:45
Бранко РБранко Р
312
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answered Apr 15 at 23:45
Бранко РБранко Р
312
answered Apr 15 at 23:45
Бранко РБранко Р
312
312
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$begingroup$
Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
add a comment |
$begingroup$
Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
$begingroup$
Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
$begingroup$
Vlad can also lie that he is Michael, and there is no correlation between the doors and the guards, and also, the information given is true, there is no need to doubt that. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:11
add a comment |
$begingroup$
You just need one question and u have to use the stone.
Ask the most left guard:
"What would the middle guard answer, if I would ask him:
What would the right guard answer, if I would ask him what's the door to hell"
(crazy question but I needed to include all 3 guards in one question)
With the stone, the event with the lowest chance would be that 2 guards will tell the truth and one will lie. -> The asked guard will lie -> He points on the door to heaven! -> 100% chance to go to heaven!
edited Apr 16 at 17:50
Rubio♦
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
311
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add a comment |
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You just need one question and u have to use the stone.
Ask the most left guard:
"What would the middle guard answer, if I would ask him:
What would the right guard answer, if I would ask him what's the door to hell"
(crazy question but I needed to include all 3 guards in one question)
With the stone, the event with the lowest chance would be that 2 guards will tell the truth and one will lie. -> The asked guard will lie -> He points on the door to heaven! -> 100% chance to go to heaven!
edited Apr 16 at 17:50
Rubio♦
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
311
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add a comment |
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You just need one question and u have to use the stone.
Ask the most left guard:
"What would the middle guard answer, if I would ask him:
What would the right guard answer, if I would ask him what's the door to hell"
(crazy question but I needed to include all 3 guards in one question)
With the stone, the event with the lowest chance would be that 2 guards will tell the truth and one will lie. -> The asked guard will lie -> He points on the door to heaven! -> 100% chance to go to heaven!
edited Apr 16 at 17:50
Rubio♦
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
311
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guest1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
You just need one question and u have to use the stone.
Ask the most left guard:
"What would the middle guard answer, if I would ask him:
What would the right guard answer, if I would ask him what's the door to hell"
(crazy question but I needed to include all 3 guards in one question)
With the stone, the event with the lowest chance would be that 2 guards will tell the truth and one will lie. -> The asked guard will lie -> He points on the door to heaven! -> 100% chance to go to heaven!
edited Apr 16 at 17:50
Rubio♦
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
311
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edited Apr 16 at 17:50
Rubio♦
30.6k567188
edited Apr 16 at 17:50
Rubio♦
30.6k567188
edited Apr 16 at 17:50
Rubio♦
30.6k567188
30.6k567188
answered Apr 16 at 14:52
guest1234guest1234
311
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answered Apr 16 at 14:52
guest1234guest1234
311
answered Apr 16 at 14:52
guest1234guest1234
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311
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add a comment |
add a comment |
$begingroup$
Just ask the room
"Which is the door to heaven?" while using the stone. The least likely outcome is that Vlad will answer you truthfully, so whoever answers you is Vlad, and he's telling you the correct door.
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
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add a comment |
$begingroup$
Just ask the room
"Which is the door to heaven?" while using the stone. The least likely outcome is that Vlad will answer you truthfully, so whoever answers you is Vlad, and he's telling you the correct door.
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
$endgroup$
add a comment |
$begingroup$
Just ask the room
"Which is the door to heaven?" while using the stone. The least likely outcome is that Vlad will answer you truthfully, so whoever answers you is Vlad, and he's telling you the correct door.
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
$endgroup$
Just ask the room
"Which is the door to heaven?" while using the stone. The least likely outcome is that Vlad will answer you truthfully, so whoever answers you is Vlad, and he's telling you the correct door.
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
answered Apr 15 at 17:50
Nuclear WangNuclear Wang
1,312616
1,312616
add a comment |
add a comment |
$begingroup$
Well, the post by StephenTG is correct without asking questions.
Following the hint, here's my answer for if you HAVE to ask a question.
Because Vlad LIES 90% of the time, then he's truthful 10% of the time. Therefore, by using the stone to make that 10% happen, Vlad tells the truth of which door to go through.
answered yesterday
CStafford-14CStafford-14
16310
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That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
1
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
add a comment |
$begingroup$
Well, the post by StephenTG is correct without asking questions.
Following the hint, here's my answer for if you HAVE to ask a question.
Because Vlad LIES 90% of the time, then he's truthful 10% of the time. Therefore, by using the stone to make that 10% happen, Vlad tells the truth of which door to go through.
answered yesterday
CStafford-14CStafford-14
16310
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That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
1
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
add a comment |
$begingroup$
Well, the post by StephenTG is correct without asking questions.
Following the hint, here's my answer for if you HAVE to ask a question.
Because Vlad LIES 90% of the time, then he's truthful 10% of the time. Therefore, by using the stone to make that 10% happen, Vlad tells the truth of which door to go through.
answered yesterday
CStafford-14CStafford-14
16310
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$endgroup$
Well, the post by StephenTG is correct without asking questions.
Following the hint, here's my answer for if you HAVE to ask a question.
Because Vlad LIES 90% of the time, then he's truthful 10% of the time. Therefore, by using the stone to make that 10% happen, Vlad tells the truth of which door to go through.
answered yesterday
CStafford-14CStafford-14
16310
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answered yesterday
CStafford-14CStafford-14
16310
New contributor
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answered yesterday
CStafford-14CStafford-14
16310
answered yesterday
CStafford-14CStafford-14
16310
16310
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$begingroup$
That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
1
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
add a comment |
$begingroup$
That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
1
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
$begingroup$
That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
That would be a great idea but, you don't know who is Vlad. And yes, the questions are not required
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Can't you ask all three at once? There's one question, and you can eliminate try to decide who Vlad is. Wait... they may try to get you to think Michael is Vlad, therefore giving a 25% of lying, therefore, the stone makes it a lie...
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
$begingroup$
Vlad has the highest chance of lying, therefore, the stone will make the least likely to happen: Vlad telling the truth.
$endgroup$
– CStafford-14
yesterday
1
1
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
John would behave just like Vlad if you use the stone. Let me explain - there are two misunderstandings about the stone. First of all: the 'least likely' applies for a set of events, excluding random. Playing poker won't result in asteroid falling down. Secondly: In John's case there are two outcomes: telling the truth with 30% chance or telling a lie. Using a stone, will cause the least likely one to occur with 100% chance. Stone can be used to 'correct' one outcome, not a lot.
$endgroup$
– Andrii Chumakov
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
$begingroup$
As long as I don't ask Michael, I'm fine.
$endgroup$
– CStafford-14
yesterday
add a comment |
$begingroup$
If, contrary to StephenTG's answer, we interpret the stone as only applying to random events, then we can simply ask
Which of these doors leads to hell?
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
$endgroup$
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
add a comment |
$begingroup$
If, contrary to StephenTG's answer, we interpret the stone as only applying to random events, then we can simply ask
Which of these doors leads to hell?
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
$endgroup$
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
add a comment |
$begingroup$
If, contrary to StephenTG's answer, we interpret the stone as only applying to random events, then we can simply ask
Which of these doors leads to hell?
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
$endgroup$
If, contrary to StephenTG's answer, we interpret the stone as only applying to random events, then we can simply ask
Which of these doors leads to hell?
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
answered Apr 15 at 17:30
AcccumulationAcccumulation
554111
554111
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
add a comment |
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
$begingroup$
You might want to elaborate on your answer. MIchel will show you one door (choose this one) or the other two will show you two doors (choose the last one)
$endgroup$
– Armin
Apr 16 at 11:43
add a comment |
$begingroup$
Am I confused...It seems like asking Vlad with the stone is the best option because is has a 10% chance of telling the truth. "This stone makes the event with the lowest chance to occur". So Then Vlad tells the truth, and you leave asking only 1 question?
Then just ask Michael a couple of times for fun because you already know the truth.
Michael should agree with Vlad at least once if not more.
answered Apr 15 at 20:13
cybernardcybernard
1414
$endgroup$
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
1
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
2
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
|
show 2 more comments
$begingroup$
Am I confused...It seems like asking Vlad with the stone is the best option because is has a 10% chance of telling the truth. "This stone makes the event with the lowest chance to occur". So Then Vlad tells the truth, and you leave asking only 1 question?
Then just ask Michael a couple of times for fun because you already know the truth.
Michael should agree with Vlad at least once if not more.
answered Apr 15 at 20:13
cybernardcybernard
1414
$endgroup$
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
1
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
2
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
|
show 2 more comments
$begingroup$
Am I confused...It seems like asking Vlad with the stone is the best option because is has a 10% chance of telling the truth. "This stone makes the event with the lowest chance to occur". So Then Vlad tells the truth, and you leave asking only 1 question?
Then just ask Michael a couple of times for fun because you already know the truth.
Michael should agree with Vlad at least once if not more.
answered Apr 15 at 20:13
cybernardcybernard
1414
$endgroup$
Am I confused...It seems like asking Vlad with the stone is the best option because is has a 10% chance of telling the truth. "This stone makes the event with the lowest chance to occur". So Then Vlad tells the truth, and you leave asking only 1 question?
Then just ask Michael a couple of times for fun because you already know the truth.
Michael should agree with Vlad at least once if not more.
answered Apr 15 at 20:13
cybernardcybernard
1414
answered Apr 15 at 20:13
cybernardcybernard
1414
answered Apr 15 at 20:13
cybernardcybernard
1414
answered Apr 15 at 20:13
cybernardcybernard
1414
1414
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
1
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
2
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
|
show 2 more comments
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
1
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
2
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
$begingroup$
How do you know who is Vlad and who is not?
$endgroup$
– Eagle
Apr 15 at 20:16
1
1
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
@Akari Hmmm He's the one with the Russian accent. Suppose that would be too easy.
$endgroup$
– cybernard
Apr 15 at 20:18
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
$begingroup$
Are you sure that there can never be any Russians with Michel or John as their names? And that Vlad is definitely Russian?
$endgroup$
– Eagle
Apr 15 at 20:19
2
2
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
$begingroup$
@SamyBencherif Jokes on you, it's Vlad the Impaler, thus Romanian/Transylvanian xD
$endgroup$
– Armin
Apr 16 at 11:42
1
1
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
$begingroup$
@cybernard, please, do not rely on russian accent to deduce who is who. I'll make an edit, to make sure its clear. Nice try
$endgroup$
– Andrii Chumakov
Apr 16 at 15:08
|
show 2 more comments
Andrii Chumakov is a new contributor. Be nice, and check out our Code of Conduct.
Andrii Chumakov is a new contributor. Be nice, and check out our Code of Conduct.
Andrii Chumakov is a new contributor. Be nice, and check out our Code of Conduct.
Andrii Chumakov is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
Are only yes/no questions allowed?
$endgroup$
– EKons
Apr 14 at 18:56
$begingroup$
@EKons, you may ask them whatever question you want, but there is no guard, who always tells the truth, which makes it difficult to find the correct door using qs like "What's 1 + 1"
$endgroup$
– Andrii Chumakov
Apr 14 at 18:59
5
$begingroup$
Michael, who tells truth with 75% chance;-- What does this even mean? That he tells the truth in 3 out of 4 situations? Or that he always believes he tells the truth, but it might not be the correct answer?$endgroup$
– Pod
Apr 15 at 9:38
2
$begingroup$
Your problem is based on a false premise. I'd rather drink beers in hell compared to being bored in clouds.
$endgroup$
– Overmind
Apr 16 at 7:09
2
$begingroup$
If I beat myself to death with the stone figuring that I am in some kind of alternate dimension figuring I will wake up in reality then what happens?
$endgroup$
– cybernard
Apr 16 at 15:14