Total Posts:59|Showing Posts:31-59|Last Page
Jump to topic:

THE Most Difficult Logic Puzzle!

Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/17/2008 11:44:16 PM
Posted: 10 years ago
Corrected version....
Of course I screwed up section (ii) of Step 1....
Here's the fixed version.

Ok, here's my approach.

It's a 3 step approach (duh). The first 2 steps are aimed at identifying (by elimination) Random. Once that is done, we establish which one of the two remaining gods (non-Randoms) is True and which one is false. This is done in Step 3.

Step 1:
Ask A the following question:

If I were to ask those of B and C who are not Random whether B is Random, would I definitely get "ja" as an answer?

(it's worded so awkwardly for a reason….trust me)

Here are the possibilities:

A can only be True, False or Random.

A says:

(i) Ja (yes)

If A is True:
B is not Random (C is Random)
Because it means that A tells us the truth about the fact that False would say that B is random (and False would lie)

If A is false:
B is not Random (because C is Random)
Because A is lying to us by saying that True would say that B is Random. This means that True would in fact say that B is NOT Random. Therefore B is not Random.

If A is Random = B is not Random (because A is Random)

(ii) Ja (no)

If A is True:
B not Random
That is because A is telling us the truth that False would not say "no" when asked if B is Random. This means that False would say "yes" if asked if B is Random. But False lies. Therefore B is not Random.

If A is False:
B not Random
That is because A is lying to us when he says that True would not say that B is not Random. Therefore True would say that B not Random. Therefore B is not Random.

If A is Random
B not Random

(iii) A says: da (yes)

A is True:
B is Random, therefore C is not Random
That is because A is telling us the truth that False would say that B is not Random. But False would lie. Therefore B is Random. Therefore C is not Random.

A is False:
B is Random, therefore C is not Random
That is because A is lying to us when he says that True would say that B is not Random. True would in fact say that B IS Random. Therefore C is not Random.

A Random
C is not Random (because A is Random)

iv) A says: da (no)

A is True:
B is Random, therefore C is not Random.
That is because A is telling us the truth when he says that False would not say that B is Random. Therefore False would say that B is not random. But false lies. Hence, B is Random. Therefore, C is not Random.

A is False:
B is Random, therefore C is not Random.
That is because A is lying to us when he says that True would not say that B is Random. Therefore True would say that B is Random. Hence, B is Random.
Therefore, C is not Random.

A is Random:
If A is Random then neither B nor C is Random.
Therefore, C is not Random

Conclusion:
If A says Ja=B not Random
If A says Da = C not Random

Step 2.
If B is non-Random, we now turn to B. If C is non-random, we now turn to C.
Assume it's B for the sake of the argument.

We ask B the same question about A&C. This will eliminate one of A&C as Random.

The question is:

If I were to ask those of A and C who are not Random whether A is Random, would I definitely get "ja" as an answer?

The logic is identical as in Step 1 except now we know that B himself is not Random. To rehash, the answers will have the following meanings:

Ja = A not Random
Da=C not Random

We can now identify one definitely non-Random god.

Step 3
We now turn to the non-Random of A&C (determined in step 2 above). Assume it's A.
We need to establish which one of A & B is True.

Here's my proposed question:

If I were to ask False whether you are Random, would he say Ja?

The objective answer is "no" (as in, A is not Random). We know that from step 2 above.

Possibilities:
A is either True or False.
B is either True or False.
We've already established (by elimination) that C is Random.

1.
A is False

a.ja is yes
False would answer "yes" (ja). A will answer "no" (da). That's because A will lie about what False (himself in this case) would say.

b.ja is no
False would answer "yes" (da). A will answer "yes"(da). That's because A will lie about what False (himself in this case) would say. Therefore A will falsely affirm the question and claim that False would answer "ja".

2. A is True

a.ja is yes
False would answer "yes" (ja). A will answer "yes" (ja). A, being True, will Affirm that False would say "yes" (ja) to the question of whether A is Random.

b.ja is no
False would answer "yes" (da). A will answer "no" (ja). A, being True, will Negate that False would say "no" (ja).

Therefore, if A answers "ja" then A is true and B is False.
If A answers "da" then A is False and B is True.
And we already know from the first 2 steps that C is Random.

I've looked over this a number of times and even did a practical demo of steps 1 and 2 with my 3 "goddesses" (my daughter, wife and mother).

I have a huge headache now and I don't want to even think about "Random" for the next two days or so.

Having said that, please have a look at this and tell me if it makes sense. I'm happy to explain.

Of course, I might be totally wrong. My logic could be totally flawed.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/17/2008 11:51:44 PM
Posted: 10 years ago
At 10/17/2008 5:43:49 PM, Lightkeeper wrote:
I think you're on the right track but I don't think this is it yet. Consider the following:

Assume A is False, B is True and C is Random (your possibility 3 - FTR)

Assume Da is yes and Ja is no.

This is then your possibility 3D.

You say that if you put the question "would you say Ja if asked if B is more likely to tell the truth than C?" to A, this would eliminate 3D if the answer is "ja".

Since B is True and C is Random (our assumption), the objective answer to the question "is B more likely to tell the truth than C?" is "yes"

But A is False and A always lies. Therefore A's answer to that question would be "no". In other words, if asked "is B more likely to tell the truth than C", A's answer would in fact be "no" (ja).

But when you ask him about whether his answer would be "no", he will lie about it and his answer to the question "would you say no?" will be "no".

But "no" in our example is represented by the word "ja".

Therefore in scenario FTR D, A would answer "ja" even though C is in fact Random.

It seems that this answer would not eliminate 3D.

Tell me if I'm wrong because it really is doing my head in LOL

Oh, I think I mixed up 3 and 4 when I was making my response tables, or something. I'll redo the responses for the whole thing and see if it works out. They should be opposite responses, since the only difference between 3 and 4 is switching the places of B and C, so I think I just mixed them up.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 12:21:18 AM
Posted: 10 years ago
It's because I changed my question slightly mid-writing. Here's the original question I used [I changed it to look more consistent with my 3rd question when I made it, guess I didn't think it all the way through].

Question was originally:
If asked whether 1+1=2, would B or C be more likely to say "Ja"?

1: T F R
1J: Asking T if F is more likely to tell truth than R.
True answer to question is no.
T will answer truthfully with No, Da

1D: Asking T if F is more likely to lie than R.
True answer to question is Yes.
T will answer truthfully with Yes, Da

2: T R F
2J: Asking T if R is more likely to tell truth than F.
True answer is yes.
T will answer truthully with yes, Ja

2D: Asking T if R is more likely to lie than F.
True answer is no.
T will answer truthfully with no, Ja

3: F T R
3J: Asking F if T is more likely to tell truth than R.
True answer is yes.
False will lie and say no, Da

3D: Asking F if T is more likely to lie than R.
True answer is no.
False will lie and say yes, Da

4: F R T
4J: Asking F if R is more likely to tell truth than T.
True answer is no.
False will lie and say yes, Ja

4D: Asking F if R is more likely to lie than T.
True answer is yes.
False will lie and say no, Ja

Therefore, the response table I gave was right, it was just for the wrong question. I guess when I checked if the new question gave the same answers as my old one, I only checked the first two scenarios before quitting ;]

The second question should be similarly formatted. Instead of a "Would you say Ja if asked whether X or Y tells the truth more often" it should be "If asked if 1+1=2, would X or Y be more likely to say Ja"

Making those changes, my solution is once again correct. I think.
JBlake
Posts: 4,634
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 12:27:57 AM
Posted: 10 years ago
I have an idea, but I don't know if it is within the rules?

What if we ask A if he will respond to the question with what means 'no' in his language. True will be unable to answer, False will be able to answer.

Therefore if A answers at all he is either False or Random. Their response would have to be yes, so we would know which means yes or no.

We ask B the same question. If he answers as well then we know A and B are either False or Random. Then we know C is True and can safely ask him if A is False, the answer would tell us the identity of the last two. (this works the same if the result were reversed and A did not answer).

The part I am stcuk on is if one answers and the other does not. Suggestions?
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 12:33:39 AM
Posted: 10 years ago
beem0r

Can you post your complete final version then? I'll look forward to see it.

And check mine too please.

There are many ways to skin a cat and we might both be correct and both different to whatever answer is on the website that posts the riddle.
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 12:35:48 AM
Posted: 10 years ago
At 10/18/2008 12:27:57 AM, JBlake wrote:
I have an idea, but I don't know if it is within the rules?

What if we ask A if he will respond to the question with what means 'no' in his language. True will be unable to answer, False will be able to answer.

Therefore if A answers at all he is either False or Random. Their response would have to be yes, so we would know which means yes or no.

We ask B the same question. If he answers as well then we know A and B are either False or Random. Then we know C is True and can safely ask him if A is False, the answer would tell us the identity of the last two. (this works the same if the result were reversed and A did not answer).

The part I am stcuk on is if one answers and the other does not. Suggestions?

We're meant to ask only yes/no questions. So if we ask a question that a party can't answer, we breach the rules. At the same time, why do you suggest that they couldn't answer the question you're proposing? What exact question are you proposing?
JBlake
Posts: 4,634
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 12:50:47 AM
Posted: 10 years ago
Asking "Will you answer 'no' to this question in your language?"

True will not be able to answer because in answering no in his language he would be lying, because he is indeed answering in his language. In answering yes in his language he would also be lying because he would not be answering no in his language.

I didn't read from the puzzle that we could not ask questions they would not be able to answer.
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 1:06:45 AM
Posted: 10 years ago
At 10/18/2008 12:50:47 AM, JBlake wrote:
Asking "Will you answer 'no' to this question in your language?"

True will not be able to answer because in answering no in his language he would be lying, because he is indeed answering in his language. In answering yes in his language he would also be lying because he would not be answering no in his language.

I didn't read from the puzzle that we could not ask questions they would not be able to answer.

Are you saying you don't believe that yes/no questions are required by the puzzle or that you missed that bit in the puzzle?

As for the question "Will you answer 'no' to this question in your language?".... hmm..... it screws with my head LOL....
After thinking about this thing all day my head is easy to screw with ...

Leave out the part "in your language" just for now. Ask anyone the question "Will you answer 'no' to this question"? No matter if they are True or False, they will not be able to answer the question.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 1:20:41 AM
Posted: 10 years ago
#. A B C

1. T F R
2. T R F
3. F T R
4. F R T
5. R T F
6. R F T

J. Ja is yes, Da is no.
D. Da is yes, Ja is no.

QUESTION 1

To God A, "If asked if 1+1=2, would B be more likely to say 'Ja' than C?"

1. T F R
1J. Da [no]
1D. Da [yes]

2. T R F
2J. Ja [yes]
2D. Ja [no]

3. F T R
3J. Da [no]
3D. Da [yes]

4. F R T
4J. Ja [yes]
4D. Ja [no]

5. R T F
5J. ? [?]
5D. ? [?]

6. R F T
6J. ? [?]
6D. ? [?]

Remaining choices after Question 1:

If Q1 = Ja:

2. T R F
4. F R T
5. R T F
6. R F T

If Q1 = Da:

1. T F R
3. F T R
5. R T F
6. R F T

If Q1 = Ja, we know God C is not random.
If Q1 = Da, we know God B is not random.

Same type of question for Q2, but this time, we avoid asking random by asking it to the God we know is not Random.

QUESTION 2

FOR Q1 = Ja

To God C, "If asked if 1+1=2, would A be more likely to say 'Ja' than B?"

2. T R F
2J. Da [no]
2D. Da [yes]

4. F R T
4J. Da [no]
4D. Da [yes]

5. R T F
5J. Ja [yes]
5D. Ja [no]

6. R F T
6J. Ja [yes]
6D. Ja [no]

FOR Q1 = Da

To God B, "If asked if 1+1=2, would A be more likely to say 'Ja' than C?"

1. T F R
1J. Da [no]
1D. Da [ues]

3. F T R
3J. Da [no]
3D. Da [no]

5. R T F
5J. Ja [yes]
5D. Ja [no]

6. R F T
6J. Ja [yes]
6J. Ja [no]

Remaining choices after Question 2

If Q1 = Ja and Q2 = Ja

5. R T F
6. R F T

If Q1 = Ja and Q2 = Da

2. T R F
4. F R T

If Q1 = Da and Q2 = Ja

5. R T F
6. R F T

If Q1 = Da and Q2 = Da

1. T F R
3. F T R

In all cases, we know which God is Random.

QUESTION 3 I'm rewriting my Q3 to somewhat match my other questions' formats

If Q1 = Ja and Q2 = Ja

To God B, "If asked if 1+1=2, would True say 'Ja'?"

5. R T F
5J. Ja [yes]
5D. Ja [no]

6. R F T
6J. Da [no]
6D. Da [yes]

If Q1 = Ja and Q2 = Da

To God A, "If asked if 1+1=2, would True say 'Ja'?"

2. T R F
2J. Ja [yes]
2D. Ja [no]

4. F R T
4J. Da [no]
4D. Da [yes]

If Q1 = Da and Q2 = Ja

To God B, "If asked if 1+1=2, would True say 'Ja'?"

5. R T F
5J. Ja [yes]
5D. Ja [no]

6. R F T
6J. Da [no]
6D. Da [yes]

If Q1 = Da and Q2 = Da

To God A, "If asked if 1+1=2, would True say 'Ja'?"

1. T F R
1J. Ja [yes]
1D. Ja [no]

3. F T R
3J. Da [no]
3D. Da [yes]

Remaining choices after Question 3

If Q 1, 2, 3 = Ja, Ja, Ja
5. R T F

If Q 1, 2, 3 = Ja, Ja, Da
6. R F T

If Q 1, 2, 3 = Ja, Da, Ja
2. T R F

If Q 1, 2, 3 = Ja, Da, Da
4. F R T

If Q 1, 2, 3 = Da, Ja, Ja
5. R T F

If Q 1, 2, 3 = Da, Ja, Da
6. R F T

If Q 1, 2, 3 = Da, Da, Ja
1. T F R

If Q 1, 2, 3 = Da, Da, Da
3. F T R
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 1:40:39 AM
Posted: 10 years ago
Your method also works, Light. Our methods actually work the same way, just your questions are a lot different than mine.

I wonder what the author of this riddle used for his questions.
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:01:35 AM
Posted: 10 years ago
They sure do, beem0r.

The whole thing is, you have to ask one what another would say so as to eliminate the need to find out what ja/da is. Your method originally was to aks A what A would say.

This riddle is very similar (but more complex I think) to this one:

"You are in prison. There are 2 doors. One leads to freedom, the other one leads to gallows. There is a guard at each door. One guard always tells the truth, the other one always lies.

We don't know which guard always tells the truth and which always lies. Neither do we know which door leads to freedom and which leads to gallows. In fact, that is what we are out to find out (for obvious reasons).

We are allowed to ask one question of one guard. That's one question in total. We get to choose which guard we ask.

What question do we ask?"
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:19:10 AM
Posted: 10 years ago
At 10/18/2008 1:06:45 AM, Lightkeeper wrote:
Leave out the part "in your language" just for now. Ask anyone the question "Will you answer 'no' to this question"? No matter if they are True or False, they will not be able to answer the question.

Actually, False can answer. By saying yes, he is lying, like he is supposed to. Also, by saying no, he is also lying. Neither answer contradicts this God's answering techniques, whereas both answers do for True.

Further, here is a quick way to solve the puzzle using this trickery:

Ask the question to the first two Gods.
True is the only one who will be unable to answer. If both Gods answer, we know that God C is True. If one does not answer, we know it is True.

So after 2 questions, we know who is true.

Then, we just ask T the following question:

"If I asked you if God X is False, would you say 'ja?'"
Where God X is either of the other two.

If God X is indeed False:
Ja being true yields a result of "Ja"
Ja being false yields a result of "Ja"

If God X is Random, and the other one is false,
Ja being true yields a result of "Da"
Ja being false yields a result of "Da"

Thus, a response of "Ja" means that God X is False and the other one is Random, whereas "Da" means that God X is Random and the other one is False.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:20:49 AM
Posted: 10 years ago
At 10/18/2008 2:01:35 AM, Lightkeeper wrote:
We are allowed to ask one question of one guard. That's one question in total. We get to choose which guard we ask.

What question do we ask?"

"Would the other fellow over there tell me that this door leads to freedom?"
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:32:25 AM
Posted: 10 years ago
At 10/18/2008 2:01:35 AM, Lightkeeper wrote:
Your method originally was to aks A what A would say.
Well, originally I used the exact same questions 1 and 2 you see now. I changed them after I came up with question 3, trying to make all my questions look similar. That's why my old result tables match my current questions, and not the questions I used the first time I posted the solution. I changed the questions, thinking the results would be the same, but I was wrong.

The questions I originally posted were bad, but the ones I actually had used before that were fine [same #1 and 2 as I'm using now].
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:35:33 AM
Posted: 10 years ago
At 10/18/2008 2:19:10 AM, beem0r wrote:
At 10/18/2008 1:06:45 AM, Lightkeeper wrote:
Leave out the part "in your language" just for now. Ask anyone the question "Will you answer 'no' to this question"? No matter if they are True or False, they will not be able to answer the question.

Actually, False can answer. By saying yes, he is lying, like he is supposed to.....

The problem here is that False will never say "yes". He will say "ja" or "da".
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:40:18 AM
Posted: 10 years ago
At 10/18/2008 2:32:25 AM, beem0r wrote:
At 10/18/2008 2:01:35 AM, Lightkeeper wrote:
Your method originally was to aks A what A would say.
Well, originally I used the exact same questions 1 and 2 you see now. I changed them after I came up with question 3, trying to make all my questions look similar. That's why my old result tables match my current questions, and not the questions I used the first time I posted the solution. I changed the questions, thinking the results would be the same, but I was wrong.

The questions I originally posted were bad, but the ones I actually had used before that were fine [same #1 and 2 as I'm using now].

Yup, I follow. I had the same thing. I was first looking for a neat way of having one and the same question for all 3 gods. Then I thought "but why should they all be the same?"
Lightkeeper
Posts: 50
Add as Friend
Challenge to a Debate
Send a Message
10/18/2008 2:46:29 AM
Posted: 10 years ago
At 10/18/2008 2:19:10 AM, beem0r wrote:

Actually, False can answer. By saying yes, he is lying, like he is supposed to. Also, by saying no, he is also lying. Neither answer .........:

Yup, it does make sense now that I've thought about it :)

Now.... who's gonna go and check the intended answer? LOL
LR4N6FTW4EVA
Posts: 190
Add as Friend
Challenge to a Debate
Send a Message
10/19/2008 12:23:39 PM
Posted: 10 years ago
Here's my solution:

Ask A and B the question "Will you answer "no" in your language to this question?"

If either one of them can't answer, that one is True.

If both can answer, C is true.

The last question determines the other two identities.

The question to ask would be simply to ask one of them "If you are Random, will you answer this question truthfully?" This question can only be answered by False, as Random would have to contradict himself to answer it, and therefore be both true and false.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/19/2008 7:08:53 PM
Posted: 10 years ago
At 10/19/2008 12:23:39 PM, LR4N6FTW4EVA wrote:
Here's my solution:

Ask A and B the question "Will you answer "no" in your language to this question?"

If either one of them can't answer, that one is True.

If both can answer, C is true.

The last question determines the other two identities.

The question to ask would be simply to ask one of them "If you are Random, will you answer this question truthfully?" This question can only be answered by False, as Random would have to contradict himself to answer it, and therefore be both true and false.

Random would still answer that question. It would answer it randomly with either a ja or a da. How would that be contradictory?

However, you could make a question that false cannot answer, like "Will you answer this question with 'yes' in your language?", and ask it to one of the unknowns.
JBlake
Posts: 4,634
Add as Friend
Challenge to a Debate
Send a Message
10/19/2008 7:51:35 PM
Posted: 10 years ago
At 10/19/2008 7:08:53 PM, beem0r wrote:
At 10/19/2008 12:23:39 PM, LR4N6FTW4EVA wrote:
Here's my solution:

Ask A and B the question "Will you answer "no" in your language to this question?"

If either one of them can't answer, that one is True.

If both can answer, C is true.

The last question determines the other two identities.

The question to ask would be simply to ask one of them "If you are Random, will you answer this question truthfully?" This question can only be answered by False, as Random would have to contradict himself to answer it, and therefore be both true and false.

Random would still answer that question. It would answer it randomly with either a ja or a da. How would that be contradictory?

However, you could make a question that false cannot answer, like "Will you answer this question with 'yes' in your language?", and ask it to one of the unknowns.

That was the same as my proposal. I allwed for Random to either answer or not answer. See my post in page 3 and see if you agree.
beem0r
Posts: 1,155
Add as Friend
Challenge to a Debate
Send a Message
10/19/2008 9:16:05 PM
Posted: 10 years ago
At 10/19/2008 7:51:35 PM, JBlake wrote:
That was the same as my proposal. I allwed for Random to either answer or not answer. See my post in page 3 and see if you agree.

As per the original problem, Random will answer Ja or Da randomly. It doesn't seem to indicate that in addition to these responses, Random sometimes randomly doesn't answer at all, so I would think Random would always give an answer.

And your original post does not indicate a question to ask to True that would determine who is who of the other two.
mastajake
Posts: 9
Add as Friend
Challenge to a Debate
Send a Message
10/31/2008 10:40:10 AM
Posted: 10 years ago
May you ask a question directing to all three of them(the gods) leaving one, either A, B, or C, to answer it?

if so i think i have the Answer to this riddle :D
One of the hardest things to learn in life is which bridge to cross and which to burn
Juggernaut
Posts: 90
Add as Friend
Challenge to a Debate
Send a Message
11/14/2008 1:28:43 PM
Posted: 10 years ago
I've heard this puzzle as there being two gods, one lying, and one telling the truth, and that was solvable. Forcing them to agree with each other was the best way to solve the puzzle. Now theres a 50-50 chance that they will all agree with each other.
wiploc
Posts: 1,485
Add as Friend
Challenge to a Debate
Send a Message
10/16/2012 4:49:59 PM
Posted: 6 years ago
"Would the god on your left agree that 2+2=4?"

If you put that question to all three gods, one of them couldn't answer. One of them, see, would have Random on his left, and wouldn't be able to predict Random's answer, and so couldn't know how to answer himself.

I don't know whether this helps, but it may be one step on the path.
sadolite
Posts: 10,006
Add as Friend
Challenge to a Debate
Send a Message
10/18/2012 6:54:19 PM
Posted: 6 years ago
There is only one god, the other two are spans of satan. No questions need be asked. That is how I would answer. I know it violates the rules. So what, the rules were made by satan. I am being asked to belive there are many gods all of which hold the same distinction even though two of the three can't be trusted. Which by definition does not make two of the three gods. I don't need to ask any questions as the true god will make himself known without saying a word. The true god would not participate in such disception.
Beware of the people who are in your circle but are not in your corner.

And with the stroke of a pen people 18 to 21 who own a gun became criminals and public enemy #1 having committed no crime and having said nothing. Just like the Jews in Germany during WW2. Must be a weird feeling.

When I hear people crying and whining about their first world problems I think about the universe with everything in it and people in wheelchairs and all of their problems go away.

By using this site, you agree to our Privacy Policy and our Terms of Use.