# Three Gods

There are three gods on an island. One god always tells the truth and another always lies. The twist which makes this more difficult is that the third god’s behavior is random. In addition, the gods, being jerks, answer in their own language and you don’t know which word (“da” or “ja”) means “yes” or “no.” You have three questions to work out which god is True, which god is False, and which god is Random.

Thank you Luca for your submission.

### 18 guesses to Three Gods

• Crabman

The first 2 questions are directed at all three Gods. Is this allowed, or can you only ask each question to 1 god? I’m presuming you can ask all three gods the same 3 questions at the same time.

1) What word means “yes”?
2) Do you always tell the truth?

True will have the same answer for 1 & 2, False with have different answers for 1 and 2.

Question 3 is only directed at one god.

If two Gods responded with same answer for q1 as q2 (doesnt matter if they had different answers from each other) we know the other one is False. You can then ask him/her which of the other 2 gods is True. Since you know he lies, you know the one he doesn’t identify is True.

If two Gods responded with different answers for q1 & q2, we know the other one is True. Ask him/her which one is False and he’ll tell you the truth.

• Crabman

To simplify it, the third question can be pre-determined as “Which God is Random?”. Using the same logic I described before you only pay attention to either the God you know is True or the one you know is false.

• It is important to always keep within the yes and no question parameter.
“Which god is random” and “what word means yes” would not have a response.
Crabman keep on trying. This one is a logic mind bender and you have not found the solution yet.

• Crabman

Ah… It never said only yes/no questions, but understood… fair enough. I have to run, but almost have it. Be back later if no one beats me to it.

• brent

Leveraging from Crabman’s thinking…

1) (to all gods) Do you always tell the truth?
at least 2/3 of the gods will answer in the affirmative. The one who does tell the truth and the one who lies. If all three do not answer the same the odd-man out is random god.
2) supposing “da” is the term for yes: “Is da the term for yes?” Now the truth god will answer da, the False god will answer ja, and the Random god will answer one of those two randomly. If the majority answer to Q 1) was ja, you would ask about ja being the term for yes instead of da in Q 2).
If there was an odd man out in Q1) (that would be the Random god) you now have all the info you need, so you can use your 3rd question to predict the winner of some sporting match and bet big! Otherwise, your final question is:
3) Noting the odd-god out from above (the one with the unique answer, be it the truth of false god) ask. Select one of the other two and ask “Is this god the Random god?” If the god you noted from question two was a Truth god and answers in the affirmative, the one you were asking about in 3) is the random god. If truth god answers in the negative then the other non-odd-god from Q 2) is the Random god.
If your odd-god out in Q2 was the False god, just reverse the reasoning for Q3 and you’ve identified the Random god.

This assume the True and False god both know who the Random god is, and possibly that the gods have insight into sporting event outcomes.

• Crabman

1) Are you a god?
2) Are you True?

True will answer same (da or ja) for 1 & 2. They are a god and they are True. False will answer different for 1 & 2. They will say they are NOT a god and they are true. Random could answer both same or different, but we know whether 1 or 2 answered same for both that response means “yes”.

If only 1 God responded same for 1 & 2, he is true. Point to one of other gods, ask “is he/she random”. They will tell the truth. If 2 gods gave the same answer, the other is false. Point to one of others and ask False if that one is “random”; the answer they give will be wrong.

This is badically same logic as my first repose, just following the iterated technical rule of all questions must be “yes/no” answers.

• Crabman, several times now I have pondered this algorithm and I am not confident that 3 questions could answer it, even if the answers are yes/no. Since random means random lets assume the third is random and with your answers we are not closer:
1) could be da ja da or da ja ja (Same for Brent, who’s first assumption is busted)
2) results in the same result da ja da or da ja ja. Both sets of answers could be the same or different, thus we are no closer to finding the answer.
I am still not completely sure of the answer given by Luca, but it narrows down the field quickly, and helps determining what is yes and no.
Keep trying! This one reminds me of introductory classes on algorithms and how even introductory concepts stretch your understanding of logic.

• Dang it. I pondered and mapped out the logic of Luca’s first question (revealing the first part of Luca’s answer):
Question 1 (to any god): If I asked you “Is that god Random?”, would you say “ja”? (This question, regardless of the answer, will let you identify a god who is not Random, i.e., one who is either True or False).
I have to disagree. Luca is forgetting the random who will answer da or ja no matter what is asked. In a 1 of 3 chance, accidentally asking random the first question determines nothing. I am going to leave this one open for further discussion.

• Crabman

I’m confused Dude. Are you saying that the intended solution is asking each of the 3 questions to only one God at a time? Or can each of the three questions be posed to all three Gods?

If the latter, I gave a solution (my third question is only asked to 1, but first 2 to all 3). If the former, I’ll think on it a bit more but don’t think it can be done because of of Random’s inconsistency.

• Crabman

Question 1 (to any god): If I asked you “Is that god Random?”, would you say “ja”? (This question, regardless of the answer, will let you identify a god who is not Random, i.e., one who is either True or False)

If we dont know if ja or da means yes, this question tells us nothing.

A) Ja = Yes, you asked True, you pointed at Random. He says Ja (Yes, he would say Yes)
B) Ja = Yes, you asked True, you pointed to False. He says Da (No, he would not say Yes)
c) Ja = Yes, you asked False, you pointed to Random. He says Da (No, but he’s lying)
D) Ja = Yes, you asked False, you pointed to True. He says Ja (Yes, but he’s lying)
E) Ja = No, you asked True, you pointed to Random. He says Ja (No, he would not say No)
F) Ja = No, you asked True, you pointed to False. He says Da (Yes, he would say No)
G) You asked Random, he could say Da or Ja

Asking False that question is a paradox if Ja = No. Does he tell the truth that he would lie, or does he lie about lying which is telling the truth?

That first question provides no information in my opinion. I could be missing something of course.

• Here is the answer Luca gave:
Question 1 (to any god): If I asked you “Is that god Random?”, would you say “ja”? (This question, regardless of the answer, will let you identify a god who is not Random, i.e., one who is either True or False).
Question 2 (to the god who is either True or False): If I asked you “Are you False?”, would you say “ja”?
Question 3 (to the same god as the last question): If I asked you “Is the first god I spoke to Random?”, would you say “ja”?

I like the logic and use of language, but we have found some holes in the answer. I would like to leave this one unsolved, until we have a consensus of whether this is the right answer or that the riddle is unsolvable. Maybe the answer just needs a bit of fixing or the riddle dude’s brain does.

• Crabman

With this “solution”, asking question 1 to only 1 of the gods (with out knowing which, and without knowing if Ja means yes or no) tells you absolutely nothing. I think he may be indicating that q1 is asked to all three gods. If that’s the case, my response on “May 14, 2015 at 4:00 AM” seams more (or at least as) straight forward.

• Luca

To make things more clear, i was a bit vague with the answer for the 1st question. It should’ve read (to all gods).
Seen that it still is just one question. (So you could ask them repeatedly to any of the gods)
Yet i’m thrilled to see someone pull it off elseway.

• Crabman

Good riddle Luca. !

• brent

If we are allowed to ask questions to all three gods at one time, I think I can solve the riddle with two questions. (I have already solved this form of the riddle using 2 questions 50% of the time, and 3 questions in all cases with my original response based on Crabman’s initial answer).
If we are only allowed to ask one question at a time to a single god, I think I can solve the riddle with three questions.

I look forward to knowing if you agree. I will use Luka’s “would you answer ‘ja’…” trick, combined with a circular idea I have come up with.

A) two questions asked to all gods.
I will label the gods A, B & C – and ask the gods to imagine themselves in a triangle shape facing inwards, such that B is to the left of A, C is to the left of B, and A is to the left of C.
Q1) – to all three: Would you answer ‘ja’ if I asked you “Is the god to your left the Random god” ?
Q2) – to all three is fine, or to either one of the non-random gods: Would you answer ‘ja’ if I asked you “Are you the Truth god” ?

Q1 allows me to identify the Random god. Certainly either the Truth god or the False god will answer “ja” to the question, indicating the Random god is to the left. The other consistent (Truth or False) god will answer “da” because the Random god is not to that god’s left. The Random god, well, random.
If the Random god answers da, there will be two “da’s” and one “ja” the Random god is to the left of the “ja” answer.
If the Random god answers ja, there will be one “da” and two “ja’s” the random god is to the right of the “da” answer.
To explain this a bit better, there will always be one reliable “ja” (Random is to my left) and one reliable “da” (random is NOT to my left – which implies Random is to my right). What ever answer ja or da there is only one of, we can assume is a reliable answer.

Now that we know which of the gods is the random god, we just need to decide which of the other two is the truth god. So we basically ask all the gods who the truth god is. We ignore the Random god, as we know they are not the truth god, and the “ja” answer to Q2 from the non Random god is the Truth god. The remaining non Random and non Truth god is the False god. – who as it turns out, by using Luca’s trick is as truthful as the Truth god.

B) three individual questions to specific gods.
This method uses the same circular system to identify the Random god as used in Q1 above. So you must understand how that work in order to appreciate this method.

Again I suggest:
I will label the gods A, B & C – and ask the gods to imagine themselves in a triangle shape facing inwards, such that B is to the left of A, C is to the left of B, and A is to the left of C.
Q1) God A, would you answer “ja” if I were to ask you if god B is the Random god?
if God A answers “da” (which implies either God A is the Random god, spewing a random “da” – Or god A is a Truth or False god saying god B is not the Random god. In all these cases, god B can not be the Random god, so I ask:
Q2 – assuming “da” to Q1) God B, would you answer “ja” if I were to ask you if god C is the Random god? – Since Q1 has determined god B is reliable (not Random) “ja” means god C is the random god, where “da” means god A is the random god. In either case, we know god B is reliable and which god A or C is Random.
Q3 – God B, would you answer “ja” if I were to ask you if you are the True god? “Ja” means B is True, “Da” means B is False
Since Q2 identified the Random god, (A or C) the remaining god can be determined.

If the answer to Q1 was ja then either god A is a reliable god saying god B is random (NOTE this implies god C is reliable). OR god A is the Random god, randomly saying ja (again, this would imply that god C is reliable). either way, if Q1 is ja, god C is reliable. in that case
Q2 – God C would you answer “ja” if I were to ask you if god A is Random?
here “ja” means A is Random. “da” means A is not Random, so B must be Random. Either way, we now know the Random god.
Q3 – God C would you answer “ja” if I were to ask you if you are the Truth god? Again, “ja” means C is Truth god, leaving the remaining non-Random god to be the False god. Or C saying “da” means C is the False god, leaving the remaining non-Random god to be the Truth god.

While I believe these to be valid solutions, they may be Random natterings…?

• Brent, thank you for the time you spent. It truly is a great answer. You are today’s winner to say the least.

• Zachary Kamin

Ok so my guess is dependent on the assumption that gods cannot answer questions that contradict their nature. So, you ask the first god in the line, “Will you answer this question in the affirmative?” Only the Random and True God can answer that. So this is used to find the false god. Once the false God is discovered (which would take at most two questions as if both the first people answer, then we know the final god is False), our (at most third question) can be posed to either of the other two Gods, “will you answer this question in the negative?” which the Truthful God cannot answer. If the God answers, s/he is the random God. If h/she does not, it is the truthful God and therefore all the identities can be discovered.