Mixing
logics and proofs
$begingroup$
this question in given in discreet mathematics by kenneth rosen.
Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes " or a "No" response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit ;the other branch leads deep into the jungle .A villager is standing at the fork in the road.what one question can you ask the villager to determine which branch to take .
so the answer to this question is given "if i were to ask you whether the right branch leads to the ruins would you answer yes?" , what i can't understand that if the villager were a liar he'd say "no" even if the road might lead the tourist to the ruins so how does this question provide a solution to the problem?
discrete-mathematics
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
$endgroup$
add a comment |
$begingroup$
this question in given in discreet mathematics by kenneth rosen.
Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes " or a "No" response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit ;the other branch leads deep into the jungle .A villager is standing at the fork in the road.what one question can you ask the villager to determine which branch to take .
so the answer to this question is given "if i were to ask you whether the right branch leads to the ruins would you answer yes?" , what i can't understand that if the villager were a liar he'd say "no" even if the road might lead the tourist to the ruins so how does this question provide a solution to the problem?
discrete-mathematics
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
$endgroup$
add a comment |
$begingroup$
this question in given in discreet mathematics by kenneth rosen.
Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes " or a "No" response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit ;the other branch leads deep into the jungle .A villager is standing at the fork in the road.what one question can you ask the villager to determine which branch to take .
so the answer to this question is given "if i were to ask you whether the right branch leads to the ruins would you answer yes?" , what i can't understand that if the villager were a liar he'd say "no" even if the road might lead the tourist to the ruins so how does this question provide a solution to the problem?
discrete-mathematics
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
$endgroup$
this question in given in discreet mathematics by kenneth rosen.
Each inhabitant of a remote village always tells the truth or always lies. A villager will only give a "yes " or a "No" response to a question a tourist asks. Suppose you are a tourist visiting this area and come to a fork in the road. One branch leads to the ruins you want to visit ;the other branch leads deep into the jungle .A villager is standing at the fork in the road.what one question can you ask the villager to determine which branch to take .
so the answer to this question is given "if i were to ask you whether the right branch leads to the ruins would you answer yes?" , what i can't understand that if the villager were a liar he'd say "no" even if the road might lead the tourist to the ruins so how does this question provide a solution to the problem?
discrete-mathematics
discrete-mathematics
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
asked Dec 5 '15 at 17:02
srishti77714srishti77714
11
11
add a comment |
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".
On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".
Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
$endgroup$
add a comment |
$begingroup$
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!
If something is wrong or ambiguous, correct me.
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
$endgroup$
add a comment |
$begingroup$
You need to differentiate between two different questions:
Q1: Does the right road lead to the ruins?
Q2: Would you say "yes" to question Q1?
If the right road does lead to the ruins, the liar will say "No" to Q1, and therefore say "Yes" to Q2!
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
$begingroup$
If you ask a liar a question the answer will be lie.
If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.
So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".
....
To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]
[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he *wouldn't give.)
====
Or you could parse it from the top down:
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"
That's a lie. He would answer yes.
- "Does the right branch leads to the ruins" LIAR: "YES"
- That's a lie. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"
That's the truth. He would answer no.
- "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
- That's the truth. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Hence "NO" means left branch.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"
That's a lie. He would answer no.
- "Does the right branch leads to the ruins" LIAR: "NO"
- That's a lie. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"
That's the truth. He would answer yes.
- "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
- That's the truth. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Hence "YES" means right branch.
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
$endgroup$
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
add a comment |
Your Answer
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".
On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".
Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
$endgroup$
add a comment |
$begingroup$
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".
On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".
Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
$endgroup$
add a comment |
$begingroup$
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".
On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".
Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
$endgroup$
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".
On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".
Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
answered Dec 9 '15 at 16:12
René B. ChristensenRené B. Christensen
46049
46049
add a comment |
add a comment |
$begingroup$
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!
If something is wrong or ambiguous, correct me.
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
$endgroup$
add a comment |
$begingroup$
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!
If something is wrong or ambiguous, correct me.
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
$endgroup$
add a comment |
$begingroup$
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!
If something is wrong or ambiguous, correct me.
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
$endgroup$
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!
If something is wrong or ambiguous, correct me.
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
answered Jul 4 '17 at 15:50
Abdelrahman TorkiAbdelrahman Torki
31
31
add a comment |
add a comment |
$begingroup$
You need to differentiate between two different questions:
Q1: Does the right road lead to the ruins?
Q2: Would you say "yes" to question Q1?
If the right road does lead to the ruins, the liar will say "No" to Q1, and therefore say "Yes" to Q2!
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
$begingroup$
You need to differentiate between two different questions:
Q1: Does the right road lead to the ruins?
Q2: Would you say "yes" to question Q1?
If the right road does lead to the ruins, the liar will say "No" to Q1, and therefore say "Yes" to Q2!
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
$begingroup$
You need to differentiate between two different questions:
Q1: Does the right road lead to the ruins?
Q2: Would you say "yes" to question Q1?
If the right road does lead to the ruins, the liar will say "No" to Q1, and therefore say "Yes" to Q2!
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
$endgroup$
You need to differentiate between two different questions:
Q1: Does the right road lead to the ruins?
Q2: Would you say "yes" to question Q1?
If the right road does lead to the ruins, the liar will say "No" to Q1, and therefore say "Yes" to Q2!
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
answered Jul 4 '17 at 16:22
Bram28Bram28
61.9k44793
61.9k44793
add a comment |
add a comment |
$begingroup$
If you ask a liar a question the answer will be lie.
If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.
So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".
....
To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]
[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he *wouldn't give.)
====
Or you could parse it from the top down:
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"
That's a lie. He would answer yes.
- "Does the right branch leads to the ruins" LIAR: "YES"
- That's a lie. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"
That's the truth. He would answer no.
- "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
- That's the truth. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Hence "NO" means left branch.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"
That's a lie. He would answer no.
- "Does the right branch leads to the ruins" LIAR: "NO"
- That's a lie. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"
That's the truth. He would answer yes.
- "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
- That's the truth. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Hence "YES" means right branch.
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
$endgroup$
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
add a comment |
$begingroup$
If you ask a liar a question the answer will be lie.
If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.
So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".
....
To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]
[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he *wouldn't give.)
====
Or you could parse it from the top down:
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"
That's a lie. He would answer yes.
- "Does the right branch leads to the ruins" LIAR: "YES"
- That's a lie. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"
That's the truth. He would answer no.
- "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
- That's the truth. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Hence "NO" means left branch.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"
That's a lie. He would answer no.
- "Does the right branch leads to the ruins" LIAR: "NO"
- That's a lie. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"
That's the truth. He would answer yes.
- "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
- That's the truth. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Hence "YES" means right branch.
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
$endgroup$
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
add a comment |
$begingroup$
If you ask a liar a question the answer will be lie.
If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.
So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".
....
To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]
[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he *wouldn't give.)
====
Or you could parse it from the top down:
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"
That's a lie. He would answer yes.
- "Does the right branch leads to the ruins" LIAR: "YES"
- That's a lie. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"
That's the truth. He would answer no.
- "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
- That's the truth. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Hence "NO" means left branch.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"
That's a lie. He would answer no.
- "Does the right branch leads to the ruins" LIAR: "NO"
- That's a lie. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"
That's the truth. He would answer yes.
- "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
- That's the truth. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Hence "YES" means right branch.
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
$endgroup$
If you ask a liar a question the answer will be lie.
If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.
So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".
....
To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]
[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he *wouldn't give.)
====
Or you could parse it from the top down:
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"
That's a lie. He would answer yes.
- "Does the right branch leads to the ruins" LIAR: "YES"
- That's a lie. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"
That's the truth. He would answer no.
- "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
- That's the truth. The right branch does not lead to the ruins.
- Conclusion: The left branch lead to the ruins.
Hence "NO" means left branch.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"
That's a lie. He would answer no.
- "Does the right branch leads to the ruins" LIAR: "NO"
- That's a lie. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"
That's the truth. He would answer yes.
- "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
- That's the truth. The right branch does lead to the ruins.
- Conclusion: The right branch lead to the ruins.
Hence "YES" means right branch.
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
edited Dec 1 '18 at 19:02
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
answered Dec 1 '18 at 18:14
fleabloodfleablood
70.2k22685
70.2k22685
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
add a comment |
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
$begingroup$
F%CK!!! Another Zombie thread!!!!! I hates them! I hates them, I tells ya!
$endgroup$
– fleablood
Dec 1 '18 at 19:03
add a comment |
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