### Can you solve the three gods riddle? - Proposed Answer

I recently landed on a youtube video about this question and intrigued about its uncertainty in detail in every aspect. Hence i thought it would be a challenge to solve it and decided to work on it.

For those who dont know about the question can watch this video to know it better.

I thought we can exploit the details of the question to workaround and come up with a decent answer to this question.

My take is as follows.

Condition 1: We can ask only three yes/no questions
Condition 2: Each question should be dedicated to only one god.
Condition 3: You can ask multiple questions to the same god.

Let us choose first god and ask the first question

1) Are you ARR?

Repeat the question again and again to confirm it is not ARR. Since you will get different responses for the same question. (Remember, Condition 1 limits the number of questions can be asked but not from the number of times it can be asked.)

If the God is ARR, We can skip to the 2nd god, otherwise we can stick with the current god.

Then we can ask the following questions.

2) Is anyone of you two is ARR? (1,2 or 2,3)

3) Did you say ozo/zulu(based on the previous response) to my previous question.
If the answer is same as the previous question. Then I am talking to Tee(next to him is ARR and next to ARR is Eff)
If the answer is different, then i am talking to Eff(next to him is Tee and next to Tee is ARR)

And we can deduce what is ozo and zulu based on our previous deductions.

Note : We can switch subject names in the question based on multiple scenarios to deduce the answer. I didn't want to confuse you further. I would like you to get the logic behind the questionnaire. So that you can play out different scenario with the question pattern and blow out your mind.

Note : The objective of the problem is to find which is which god and what are the equivalents of yes and no. without exhausting the number of questions.

Then we can talk to the most reliable god Tee to get a free uplift from their planet.

I believe this would be a better answer. Since other answers are mostly speculative and is mostly vulnerable against ARR.

It is said ARR is Random. Which means ARR can provide any answer (True, False, True, True, False). Hence you might end up in a scenario where ARR pretty much fake like it is TEE or EFF. Your well tailored question might be lost on ARR and your number of chances even get reduced to 2 or 1. Definitely, there is no logical solutions that can filter out ARR within 3 attempts.
And there is no guarantee that the first one you interact would not be ARR.

Last but best part,

It took me 3 hours to completely understand and come up with a mere solution. And the video asks me to come up with a solution is 3 seconds.

Seriously :)

Anyway guys(Ted ed). Good Job on your video. 3 hours well spent.

1. Few things.
- interesting solution/workaround. The rules indeed do not state 'restating the same question' counts as a new question. Nice catch.

However as for the objective: no 'finding out "what are the equivalents of yes and no" 'is not part of the objective. just a useful tool (if it wouldn't lead to exhausting the questions)

The 'the video asks me to come up with a solution in 3 seconds'-statement is not entirely correct. It explicitly states you SHOULD pauze the video if you want to figure it out yourself

If there is one part i consider a problem, it's the blatant statement you refuse to buy other answers.
I mean, the following statement 'Arr can fake it' is true, but the conclusion:
'Definitely, there is no logical solutions that can filter out ARR within 3 attempts'
is not.
True, it can't be done by talking TO Arr, but about Arr, that IS possible.

1. The comment about 3 seconds is just a joke.

The reason i told i cant buy other answer is the answers i read from different persons are mathematical and logical models and they can't help solve the ARR problem as they can't rule out ARR within 3 attempts.

But when i looked up on your answer on the comment section of the video, i am completely blown out. Seriously your answer is simply the best.

2. Pardon me. I am confused with you and Tim Freeman. Its Tim Freeman's answer

2. Hoping the 'i won't buy...'-statement doesn't mean 'i won't even look at', i'll take a crack at it.

First taking the assumption (which i also made) the 'which word means 'yes'' is relevant (it is relevant, it will just turn out not to be required) there are 12 possible scenarios
'means yes', 'ordering of the gods'
ozo , TFR - ulu , TFR
ozo , TRF - ulu , TRF
ozo , FRT - ulu , FRT
ozo , FTR - ulu , FTR
ozo , RTF - ulu , RTF
ozo , RFT - ulu , RFT
However, with 3 binary questions, we can only identify 8 (2^3) subsets of this.
So without 'some kind of trick' this can't be done.

Here i must once again say, 'nice catch' on the trick you found. (no rule against restating the same question)

As the stated goal doesn't require the ozo/ulu situation to be resolved, giving us the 6 subsets to be figured out: RTF, RFT, FTR, FRT, TRF, TFR. IF we can find a way to take ozo/ulu thing out of it. (without spending a question on it)

Which fortunately we can:
Decide which one you'll consider to mean 'yes' regardless of whether this is accurate. (i'm going with ozo, for the example)

Is exactly 1 of the following statements correct?:
- [the question you actually want to ask]
- does ozo imply NEGATIVE confirmation (would mean 'no', but we need to paraphrase as we can't translate that word)

the 4 possible scenarios here are
- ozo means yes, and the answer to your question is yes -> exactly 1 is true: yes -> ozo
- ozo means no , and the answer to your question is yes -> NOT exactly 1 is true(they both are): no -> ozo
- ozo means yes and the answer to your question is no -> neither 1 is true: false -> ulu
- ozo means no and the answer to your question is no -> exactly 1 is true: true -> ulu

Having shown the ozo/ulu situation can be taken out, i'll leave that one.

1. No. when i thought the solution is not possible, i had searched for the answer on the internet and read a lot of answers try to solve it mathematically or logically which is not possible without ruling out the ARR factor with certainity. Thats why i told that i am not buying them.

3. Now we have 6 scenarios to deal with and 3 binary questions to do it (seems possible: still not trivial though)
We still have one that lies and one that's honest (your remark, all answers coming from Arr are useless, is accurate, so look at the other 2 for a moment)
Also that one can be taken out if formulated carefully (we still need to tell them apart, as that IS the riddle, but as far as the answers are concerned), fortunately, that's a well known riddle '2 stand at a fork in the road, ask one "what would the other (non Arr) tell me?" act on the opposite (to find the correct path to the city)'.

This leaves us with a means to ask anything from the gods and getting a clear, truthful answer unless we're addressing Arr (this issue remains valid and will be resolved shortly).

As the video shows, these 2 'wrappers' can be combined into 'if i were to ask ________, would your answer be ozo?' (way more elegant than the way i put it, i hope my breakdown was useful in showing what it would do)

So now to the question within the 'would you answer'-wrappers.
We have 3 of them, answers from Arr are useless and we have 6 scenarios to pull apart.
Address the 1st one (how you define first, is irrelevant):
at this point you have all 6 scenarios as possible RTF, RFT, TFR, TRF, FRT, FTR.
No matter what you ask, no matter what answer you get: RTF and RFT remain possible (answers from Arr are useless), so we need to split the other 4 both 'evenly' as 4 scenarios with 2 binary questions is the max that can be resolved and somehow guarantee we will not address another question to Arr (which would bring us back to the same issue)
So ask if #2 is Arr (with the 'would you answer ozo'-wrapper)
If so: [RTF, RFT, TRF, FRT] are the remaining possibilities, of not [RTF, RFT, TFR, FTR] are.
Either way, you have 4 scenarios, 2 binary questions AND 1 god identified as 'not Arr' which is what we need to take the maximum(or anything, basically) out of those 2 questions.
Which is enough ('is #1 Arr', and 'are you Tee' will do)

1. I get it Michael. I get it where i messed it up. Really appreciate your efforts on helping me out here. Kindly do share your blog address so that i can follow and catch up with you.

4. The assumption that asking one question repetitiously does not count as asking additional questions is shaky at best. A bit clever, but more than a little shaky. You ask a question, you direct it toward a given target, and the target gives you an answer. That's one question. Repeating it is still asking more questions. It's not their fault if you waste your questions on recycling.

Let's say that your assumption was given as true. Technically, no matter how many times you ask, you are never entirely sure that you are not dealing with Arr. As you repeat your question and get the same answer, you decrease the odds of it being Arr, but Arr \could/ be randomly selecting the same answer over and over. You may very well be satisfied with incredible odds after asking one hundred consecutive times or something, but we should be fair in saying that this solution, even without any other kinks, is an inferior one simply because it requires you to choose your own odds that can never be totally guaranteed.

Your second question would be better phrased as, "Is either of you two Arr?" *pointing at 1 and 2 or 2 and 3*

As Michael pointed out, your third step is where you absolutely fall apart, because you can not confidently establish either variable by it.

You say at the end that you talk to Tee for the ride off the planet, but the described scenario is one in which your only allowed communication is three questions, and the method of leaving the planet involves giving each of the three targets their own artifact. I suppose that that tidbit is separate from the body of what you're doing, though.

1. Yeah, I get it. Seems i had jumped the wagon on that part. I had missed the other scenario.
And
I assumed identifying gods would be enough as i don't think extracting all the required details within three questions is a plausible scenario.
I really appreciate both of you for your efforts at helping me out here. Let me try again to get it further. Thanks for both of your help. :)

5. Great post thank youu