excreationist

It is simpler to just ask "do you understand English?" and keep on asking and seeing if they ever answer "no" by accident.

I don't think that is a satisfactory solution though since I said that you could only ask a limited number of questions and there would always be a small chance that the person seems to understand English because they are guessing right. So that is not a proof, though it would work in most cases.

Basically if the person answers in an inconsistent way, they definitely don't understand English, but if they answer consistently (e.g. they say "yes" to "do you understand English?"), you can't be certain whether they understand English or not.

BTW, I misunderstood the original question... I thought that Random had no understanding of the question it was asked, but it actually does and it flips a coin to decide to lie or speak truly.

[ March 23, 2002: Message edited by: excreationist ]</p>

phaedrus

Umm, actually this puzzle shot into fame in the book "Logic, Logic, Logic" by George Boolos. The puzzle is attributed to Raymond Smullyan and the modification of which are the gods’ words for “yes” and “no” was added by John McCarthy.

The law of excluded middle comes into play ?

Samhain

I think I solved it...

"What do you mean, an African or a European swallow?"

Give me my prize and let me cross the Bridge o' Death

Boro Nut

Trust philosophers to miss the point. The solution actually very simple.

1) Hold gun to first God's head and ask him which one he is.

2) When he answers, point the gun at one of the other Gods and shoot him.

3) Hold the gun to his head again and say, "I'm not fucking about you know. Which God are you?"

4) When he answers you will be able to tell if he is the random god or not.

5) Without saying anything, point the gun at the other god, and he will instantly verify which Gods they both are, without being asked.

6) You have not only solved the problem but can use your remaining question to discover the meaning of life, or make a wish.

Boro Nut

Bill Snedden

Okay, here's the solution I worked out. I can't claim to have come to it 100% on my own (I had a couple of hints), but it does seem to work.

The "trick", if you will, is to word the questions such that their truth value is either known to you in advance or so constructed that the answers will assist you in eliminating false possibilities. The first step is to attempt to "weed out" the randomly answering god. I started by making a working assumption that A was either the truthful or the false speaking god and addressed my first question to A.

Question one: Does "ja" mean "yes" if you are always truthful AND god B always replies randomly?

The question has three parts, all of which work together to ensure that the truth value of the last part is determined by the answer.

Here are the possibilities based on the assumption that A is always truthful:

1) "ja" means "yes", A is truthful, and B is random - JA

2) "ja" means "yes", A is truthful, and B is not random - DA

3) "ja" means "no", A is truthful, and B is random - JA

4) "ja" means "no", A is truthful, and B is not random - DA

Obviously, the answers are reversed (da for ja) if A is assumed to be false.

So, regardless of the actual meaning of "ja" and "da", a "ja" answer tells us that B is the random god and that A & C are the true/false gods and a "da" answer tells us that C must be the random god and that A & B are the true/false gods.

Of course, this is going on the beginning assumption that A is either true or false. However, if A is in fact the random god, we know that neither B nor C can be. So, we can still proceed based on a couple more assumptions. If A is random and answers "ja", we'll make a working assumption that C is not random. If A is random and answers "da", we'll make the assumption that B is not random. (These assumptions are based on the possibilities table, above.)

So, if we get a "ja" response, we can assume that C is either true or false and if we get a "da" response, we can assume that B is either true or false.

Okay, now on to question two. I asked god B, but you can also ask god C.

Question two: Does "ja" mean "yes" if 2+2=4?

Obviously the truth value of 2+2=4 is already known, so the answer will tell us if B is true or false and it will also give us the meaning of "ja" and "da"!

A "ja" response tells us that B is the truthful god and a "da" response tells us that B is the false god.

Now that we have determined the status of one of the gods, and the meaning of "ja" and "da", we can use that knowledge to phrase a question that will allow us to determine the status of the other two.

Question three: If B is the false god, ask, Is A always truthful?. A "ja" response" indicates that A is, in fact random and so the order is A-random, B-false, C-true. A "da" response indicates A-truthful, B-false, C-random.

If B is the true god, ask, is A always false?. Again, a "ja" response gives us A-false, B-true, C-random and a "da" response yields A-random, B-true, C-false.

Ta-da!

At least, I think so. I can't work out any scenarios where this strategy doesn't seem to work.

How did I do, Kachana?

Bill

[ March 25, 2002: Message edited by: Bill Snedden ]</p>

John Page

For crying out loud they're dogs you idiot, you're barking up the wrong tree. There are no gods, this is a hard core atheist site, not a bunch of kitty litter.

phaedrus

The original solution :

First question to A

Does da mean yes iff, you are True iff B
is Random?

(iff = If and only if)

Second question to B

Does da mean yes iff Rome is in Italy?

Third question to C

Does da mean yes iff A is Random?

[ March 25, 2002: Message edited by: phaedrus ]</p>

Bill_C

Bill Snedden,

I am fairly sure that based upon this question, you cannot achieve a solution (if you can determine the meaning of ja or da). The reason being that if this question would give you the meaning of the words ja and da and and with your other two question you determine the identies of the Gods, you would have determined one of 12 possiblities witth 3 quesions. The identities of the Gods and the meaning of ja an da would span 12 possibilities (ln(12)/ln(2) = 3.58 bits). Further, three binary questions can span at most 8 possibilities (3 bits). So I am afraid your solution appears to violate information theory limits on what can be learned from three binary questions. The bottom line is I don’t think it is possible to know the meaning of da and ja and be sure that you know the identities of the Gods for all possible permutations. My first attack on the problem was to use a question similar to question 2 until I thought of this.

To understand your solution I would like to go through the 12 possibilities, but I am a little unsure of how to take your questions. My understanding of the question of the form “Is if X then Y true?” which I note as X =&gt;Yis given by the following truth table.

X Y | X=&gt;Y
F F | T
F T | T
T F | F
T T | T

Your first question is:
I take this to question to mean, “Does X imply Y” where X means (A=T and B=R) and Y means (ja = yes).
The way I would take the possibilities you illustrate is given below (note that I have rearranged the question order from your post.

X Y X=&gt;Y

4) F F T=da
2) F T F=da
3) T F F=ja
1) T T T=ja

Maybe you mean if and only if. I guess I am having a little trouble unpacking the questions and applying them. Would you illustrate your solution with the 12 possibilities? I’ll get back to your solution when I have some time.

ABC with Ja = yes
TRF ja,
TFR da
RTF
RFT
FTR
FRT

ABC with Ja = no
TRF da
TFR ja
RTF
RFT
FTR
FRT

By the way, do you think my solution is correct? You seemed to have some questions about it. I hope that my answer made sense to you.

Bill

[ March 26, 2002: Message edited by: Bill_C ]

[ March 26, 2002: Message edited by: Bill_C ]

[ March 26, 2002: Message edited by: Bill_C ]</p>

John Page

I don't have a clarification yet to my question above. While some of you might think I was being flippant, I do not think we can arrive at a logically tenable solution to the puzzle without a more complete specification of the 'gods' concerned.

Consider, for example, how can all the gods know what all the other gods know? If one of them is all-knowing then the others couldn't know what it knew and couldn't answer accurately.

"Truth" is a value that is subjective to the being thinking it (gods or not) and is established based on the information available. Thus, each "god" will answer according to what it believes and beliefs are changeable.

Perhaps it would be interesting to work back from solutions to impute what the gods must be and whether the gods are logically tenable! (I'm especially interested in the phenomenology of the random god).

Presently I have GIGO. Garbage In, Garbage Out. (Or maybe that should be God In, God Out, or maybe Garbage In, God Out or even God In, Garbage Out.)

Cheers!

Bill_C

Phaedrus,

You must have left of the description of a layer of embedded questions or something. Let me know if I understand properly? First of all a question of the form “Does X iff Y?” corresponds to the following truth table;
X Y X&lt;=&gt;Y
F F T
F T F
T F F
T T T

Now consider following two scenarios.

Case1:
da = Yes
ABC = TRF
and
Case2
da = Yes
ABC = RFT

If I read your questions directly, it appears that I can have the same answers for both sets of assignments.

Case 1
Question 1 to A : Does (da = yes)&lt;=&gt;((A=T)&lt;=&gt;(B=R))?
Since all of these quantities are true the implication holds (see truth table). Also A is a truthteller, so the answer is da.

Question 2 to B: Does (da=yes)&lt;=&gt;(Rome is in Italy)?
Again both quantities are true so the implication holds, a true answer is da. However, the God answering is random and may say either ja or da.

Question 3 to C: Does (da=yes) &lt;=&gt; (A is Random)?
Since A is not Random the implication is false. A true answer would be ja. However, C is False so the response is da.

Case 2:
Question 1 to A : Does (da = yes),&lt;=&gt;((A=T)&lt;=&gt;(B=R))?
Since B = not R and A is not T, the rightmost yields true. Since the leftmost is true (da=yes) the entire implication is also true, So a true answer gives is da. But since A=R the response could be either da or ja.

Question 2 to B: Does (da=yes)&lt;=&gt;(Rome is in Italy)?
Both quantities are true so the implication holds, a true answer is da. The God answering is False and will say ja.

Question 3 to C: Does (da=yes) &lt;=&gt; (A is Random)?
This implication holds, so the correct answer is da. The God answering is True and will respond da.

It seems that these are two cases that could both result in da, ja, da. Am I missing something?

Bill

[ March 26, 2002: Message edited by: Bill_C ]</p>