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Re: The three gods riddle (Extremely Difficult)

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pokemonmaster914 is not online. pokemonmaster914
Joined: 15 Jan 2011
Total Posts: 9115
26 Sep 2012 03:12 PM
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

-It could be that some god gets asked more than one question (and hence that some god is not asked any question at all)

-What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

-Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely

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Calao is not online. Calao
Joined: 11 May 2010
Total Posts: 8043
26 Sep 2012 03:13 PM
nice copy and paste

you dont even have the answer for it, do you
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kiddeku is not online. kiddeku
Joined: 03 Jan 2010
Total Posts: 1321
26 Sep 2012 03:14 PM
Boolos provided his solution in the same article in which he introduced the puzzle. Boolos states that the "first move is to find a god that you can be certain is not Random, and hence is either True or False".[1] There are many different questions that will achieve this result. One strategy is to use complicated logical connectives in your questions (either biconditionals or some equivalent construction).
Boolos' question was to ask A:
Does da mean yes iff you are True iff B is Random?[1]
Equivalently:
Are an odd number of the following statements true: you are False, da means yes, B is Random?
It was observed by Roberts (2001) -- and independently by Rabern and Rabern (2008) -- that the puzzle's solution can be simplified by using certain counterfactuals.[3][4] The key to this solution is that, for any yes/no question Q, asking either True or False the question
If I asked you Q, would you say ja?
results in the answer ja if the truthful answer to Q is yes, and the answer da if the truthful answer to Q is no (Rabern and Rabern (2008) call this result the embedded question lemma). The reason it works can be seen by looking at the eight possible cases.
Assume that ja means yes and da means no.
True is asked and responds with ja. Since he is telling the truth, the truthful answer to Q is ja, which means yes.
True is asked and responds with da. Since he is telling the truth, the truthful answer to Q is da, which means no.
False is asked and responds with ja. Since he is lying it follows that if you asked him Q he would instead answer da. He would be lying, so the truthful answer to Q is ja, which means yes.
False is asked and responds with da. Since he is lying it follows that if you asked him Q he would in fact answer ja. He would be lying, so the truthful answer to Q is da, which means no.
Assume ja means no and da means yes.
True is asked and responds with ja. Since he is telling the truth, the truthful answer to Q is da, which means yes.
True is asked and responds with da. Since he is telling the truth, the truthful answer to Q is ja, which means no.
False is asked and responds with ja. Since he is lying it follows that if you asked him Q he would in fact answer ja. He would be lying, so the truthful answer to Q is da, which means yes.
False is asked and responds with da. Since he is lying it follows that if you asked him Q he would instead answer da. He would be lying, so the truthful answer to Q is ja, which means no.
Using this fact, one may proceed as follows.[3]
Ask god B, "If I asked you 'Is A Random?', would you say ja?". If B answers ja, then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers da, then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, A is not Random.
Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you True?', would you say ja?". Since he is not Random, an answer of ja indicates that he is True and an answer of da indicates that he is False.
Ask the same god the question: "If I asked you 'Is B Random?', would you say ja?". If the answer is ja then B is Random; if the answer is da then the god you have not yet spoken to is Random. The remaining god can be identified by elimination.
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pokemonmaster914 is not online. pokemonmaster914
Joined: 15 Jan 2011
Total Posts: 9115
26 Sep 2012 03:15 PM
@Calao
I got it from a book, so I copied, but didn't paste it, and I know the answer, for I solved it myself. I suggest you not assume everyone on the internet is less intelligent then you.
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DrLiliam is not online. DrLiliam
Joined: 04 Jun 2012
Total Posts: 1882
26 Sep 2012 03:15 PM
he "first move is to find a god that you can be certain is not Random, and hence is either True or False".[2] There are many different questions that will achieve this result. One strategy is to use complicated logical connectives in your questions (either biconditionals or some equivalent construction).

Boolos' question was:

Does 'da' mean yes if and only if you are True if and only if B is Random?[3]
Equivalently:

Are an odd number of the following statements true: you are False, 'ja' means yes, B is Random?

The puzzle's solution can be simplified by using counterfactuals.[4][5] The key to this solution is that, for any yes/no question Q, asking either True or False the question

If I asked you Q, would you say 'ja'?
results in the answer 'ja' if the truthful answer to Q is yes, and the answer 'da' if the truthful answer to Q is no. The reason this works can be seen by looking at the eight possible cases.

Assume that 'ja' means yes and 'da' means no.
(i) True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'ja', which means yes.

(ii) True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'da', which means no.

(iii) False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means yes.

(iv) False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q is 'da', which means no.

Assume 'ja' means no and 'da' means yes.
(v) True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'da', which means yes.

(vi) True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'ja', which means no.

(vii) False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q 'da', which means yes.

(viii) False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means no.


Using this fact, one may proceed as follows.[6]

Ask god B, "If I asked you 'Is A Random?', would you say 'ja'?". If B answers 'ja', then the answer indicates that A is indeed Random and B and C are not Random. If B answers 'da', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, A is not Random.
Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you True?', would you say 'ja'?". Since he is not Random, an answer of 'ja' indicates that he is True and an answer of 'da' indicates that he is False.
Ask the same god the question: "If I asked you 'Is B Random?', would you say 'ja'?". If the answer is 'ja' then B is Random; if the answer is 'da' then the god you have not yet spoken to is Random. The remaining god can be identified by elimination.

[edit] Random's behaviour
Most readers of the puzzle assume that Random will provide completely random answers to any question asked of him; however, the puzzle does not actually state this. In fact, Boolos' third clarifying remark explicitly refutes this assumption.

Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
This says that Random randomly acts as a liar or a truth-teller, not that Random answers randomly.

A small change to the question above yields a question which will always elicit a meaningful answer from Random. The change is as follows:

If I asked you Q in your current mental state, would you say 'ja'?[6]
We have effectively extracted the truth-teller and liar personalities from Random and forced him to be only one of them. This completely trivializes the puzzle since we can now get truthful answers to any questions we please.

1. Ask god A, "If I asked you 'Are you Random?' in your current mental state, would you say 'ja'?"
If A answers 'ja', then A is Random:


2a. Ask god B, "If I asked you 'Are you True?', would you say 'ja'?"
If B answers 'ja', then B is True and C is False.

If B answers 'da', then B is False and C is True. In both cases, the puzzle is solved.

If A answers 'da', then A is not Random:


2b. Ask god A, "If I asked you 'Are you True?', would you say 'ja'?"
If A answers 'ja', then A is True.

If A answers 'da', then A is False.


3. Ask god A, "If I asked you 'Is B Random?', would you say 'ja'?"
If A answers 'ja', then B is Random, and C is the opposite of A.

If A answers 'da', then C is Random, and B is the opposite of A.


We can modify Boolos' puzzle so that Random is actually random by replacing Boolos' third clarifying remark with the following.

Whether Random says 'ja' or 'da' should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he says 'ja'; if tails, he says 'da'.

With this modification, the puzzle's solution demands the more careful god-interrogation given at the end of the The Solution section

~The best time to wear a striped sweater is all the time~
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spink00 is not online. spink00
Joined: 01 Sep 2009
Total Posts: 3756
26 Sep 2012 03:15 PM
What is one plus one?
If two answer the same, you will have found out one identity.
What is two plus two?
If one changes their answer, you have the random one.
I won.
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Calao is not online. Calao
Joined: 11 May 2010
Total Posts: 8043
26 Sep 2012 03:15 PM
well you're a christian

so you're obviously of less intelligence
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rachetandclank2 is not online. rachetandclank2
Joined: 27 Feb 2009
Total Posts: 10812
26 Sep 2012 03:16 PM
Check each answer for a pattern.
For example:

A - Daja B - Jada C - Jada

A - Daja B - Jada C - Jada

A - Daja B - Jada C - Daja


There you go.

The question is "Am I speaking to you?"
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pokemonmaster914 is not online. pokemonmaster914
Joined: 15 Jan 2011
Total Posts: 9115
26 Sep 2012 03:17 PM
@Calao
False, my religious beliefs have little to nothing to do with my intellect, for example, Isaac Newton was a devout Christian, but he was quite smart.
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Calao is not online. Calao
Joined: 11 May 2010
Total Posts: 8043
26 Sep 2012 03:18 PM
lol funny
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DrLiliam is not online. DrLiliam
Joined: 04 Jun 2012
Total Posts: 1882
26 Sep 2012 03:18 PM
"well you're a christian
so you're obviously of less intelligence"

this

~The best time to wear a striped sweater is all the time~
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pokemonmaster914 is not online. pokemonmaster914
Joined: 15 Jan 2011
Total Posts: 9115
26 Sep 2012 03:20 PM
@Cal
I was not making a joke, Isaac Newton had a reputation, still does, for being very intelligent.
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rachetandclank2 is not online. rachetandclank2
Joined: 27 Feb 2009
Total Posts: 10812
26 Sep 2012 03:20 PM
Couldn't you just figure it out by ask each god if they are speaking truthfully?

A - Ja B - Da C - Ja
A - Da B - Da C - Ja
A - Da B - Da C - Ja

This riddle is more about luck than any relative skill, Random could speak the same answer three times.
Make an actual riddle than base the outcome on luck.
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purnk78 is not online. purnk78
Joined: 18 May 2010
Total Posts: 2191
26 Sep 2012 03:20 PM
Ask the truth god:

"Are you god A?"

"Are you god B?"

"Are you god C?"

Two will be no, one will be yes.. The odd one out if yes. ;D
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ferrykeizer is not online. ferrykeizer
Joined: 14 Oct 2008
Total Posts: 31056
26 Sep 2012 03:21 PM
The answer is 6
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