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TED-Ed

TED-Ed

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Can you solve the three gods riddle? - Alex Gendler

Video Overview & Insights

View full lesson: http://ed.ted.com/lessons/can-you-solve-the-three-gods-riddle-alex-gendler

Saw this riddle somewhere on internet with just Gods named Truth, Random and Lair and instead of "ozo" and "ulu" it was "ja" and "da".

— @Shroomy_The_Crewmate

You and your team have crash-landed on an ancient planet. Can you appease the three alien overlords who rule it and get your team safely home? Created by logician Raymond Smullyan, and popularized by his colleague George Boolos, this riddle has been called the hardest logic puzzle ever. Alex Gendler shows how to solve it.

Lesson by Alex Gendler, animation by Artrake Studio.

Here's my answer 1:11

Assume :
Ozo = No, Ulu = Yes
God 1 = Blue, god 2 = Yellow, god 3 = Red

Q1 for God 1 : Is the dominant color in your body red?
If god 1 is T, answer = Ozo
If god 1 is F, answer = Ulu
If god 2 is R, answer = Ulu/Ozo

Q2 for God 2 : Is the dominant color of God 1 Red?
If god 2 is T, answer = Ozo
If God 2 is F, answer = Ulu
If god 2 is R, answer = Ulu, Ozo

Now with these questions, we can make visible patterns.

Ulu, Ozo - F, T / R, T (The gods we talked to)
Ozo, Ulu - T, F / R, F
Ulu, Ulu - F, R / R, F
Ozo, Ozo - T, R / R, T

We can see here that R has a 50% chance of being one of the gods we asked if the answers for Q1 and Q2 were opposite. But 100% chance of being one of the god we asked if the answers for Q1 and Q2 are the same.

And also the second god in (Ulu, Ozo) can only be T, while the second god in (Ozo, Ulu) can only be F.

That means we just have to ask one final question depending on what the two god answered.

Q3 to god 2 if the previous answers were (Ulu, Ozo) : Is god 1 R?
In both cases, only T can fill up God 2's spot. So it can only be the truth.
If his answer is Ozo, then God 1 is F, God 2 is T, God 3 is R.
If his answer is Ulu, then God 1 is R, god 2 is T, God 3 is F.

Q3 to god 2 if the previous answers were (Ozo, Ulu) : Is god 1 R?
This is the same as T since, in (Ozo, Ulu) god 2 can only be F. So it's always a lie.
If his answer is Ozo, then god 1 is R, god 2 is F, god 3 is T
If his answer is Ulu, then god 1 is T, god 2 is F, god 3 is T.

For the last two possibilities, we know they always have R, and missing one of the gods, but we don't know the exact order, nor which god is which.

Q3 to God 3 is the previous answers were (Ulu, Ulu) : Is god 1 R?
We know the last missing god is T, so he will always tell the truth. Meaning we just need to know who R and F is.
If his answer is Ulu, then God 1 is R, God 2 is F, God 3 is T.
If his answer is Ozo, then God 1 is F, God 2 is R, God 3 is T.

Q3 to God 3 is the previous answers were (Ozo, Ozo) : Is god 1 R?
This is basically the same thing but inverse, because F is always the missing god.
If his answer is Ozo, then God 1 is R, God 2 is T, God 3 is F.
If his answer is Ulu, then God 1 is T, God 2 is R, God 3 is F.

(This still works even if you assume Ozo as Yes, because Ozo and Ulu are just substitute for Yes and No.)

— @Ashir-S4D

More User Perspectives

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뭐라씨부리는교

@nicknamekr
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I'm just going to comment what I think it is: you ask each of them the same question which you know the answer to, then you can easily decipher it

@Baller-k2x
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Can't I just ask one of the guy if his skin color is for example green and he is green then he is the one who speaks The truth and if I ask the other alien if his skin color is for example yellow which is his skin color and he says no then he is the one who is lying.

@hanakolink.2850
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Dimag ka bhosda kardiya bhai 😭

@UhioJonn
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This is my like millionth time watching this riddle, but it literally just dawned on me now that the names of the gods are the first letter of true, false, and random

@Imamotherfreakingavocado
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Probably no one is going to see this. I tried solving this and ran into a paradox.

Lets name the aliens A B and C

I ask A "if I were to ask B and C the same question, would their answers match?"

If A is the random one then the sol9is easy from there


If either B or C is the random one, A cannot answer. What happens then? You discover a reliable one with 0 questions?

@gurosav
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Just understanding the logic burned my mind. I have no idea how smart someone had to be to think of a riddle like this let alone how someone else had to be to solve it.

@Nutsa-j6f
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I dont get it what if the middle alien is arr

@Befrman1
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I would just ask to who's artifacts is whose, since the only words I don't know are Yes or No.

@ITZRAM27
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"the liar" = (B*F) .. that is the fact! "are you the liar?" = (B*B*F) .... B will lie about being the liar. "if I ask you if you're the liar, will you say no?" = B*(B*B*F)*F. now is the tricky bit about O ... "if I ask you if you're F, will you say O?".B*(B*B*F)*O ... the truth teller just says no I'm not the liar. and that inverts O. the liar claims that he would not say no. so he's claiming he'd say yes. so he says O for O.
it wasn't clear, but asking B: "if I ask you if A is R, will you say O?" becomes B*(B* ?A==R? )*O. where ?A==R? is the fact! this is where B answers to what B would say to the fact. and if I understand, if either B or C don't say O, then they have admitted that they are R.

@woodtygr
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Uhhh…. Are you and your team by any chance the player and oatchi from pikmin 4?

@Thelilwarrior13
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So we completly ignore the fact that arr answers randomly and we continue explaning this illogically nice video!!!!

@MartaKrysztalowicz
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Today, more than 9 years after this video was punlished, i shared it with my high level esl class. Together we found an alternate way of identifying R. "Would the dude to your left tell me that the sky is blue?" Neither T or F could answer this question about R, so you would recieve silence. You have a 1/3 chance of nailing R right there. If you recieve an answer, you ask again about the dude on the right. If you recieve 2 answers you know you are talking to R. You can then follow up with the if/ would you say ulu question to figure out who is T and by process of elimination wjo is F

@natenathan2654
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I need help understanding...

If Ozo means yes, why would Eff say Yes to the question? If I ask you a question randomly without context and you're a pathological liar, you'd answer "no", right?

Also, there's a 1/3 chance one of them is Arr and any attempt might be meaningless. Either way, I think it's a die roll, and whether or not Eff knows enough to conciously want to trip us up and cover his lying.

I think this is what's tripping me up.

I think k I understand you're trying to single out Arr by having Tee and Eff use 'yes and no' on something you know the answer is 'yes'. But outside of that I'm lost how this isn't still a gamble. :(

@doositsruminile
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So if you did choose Arr for the first question, would that mean you've failed since their answer is meaningless?

@motifity3416
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hey ted,what if we ask each of the alien the same question two times,that means that the alien that gives different answers mean they are r

@vapixify-k3t
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Didn't even have to watch. The answer is false, the is one god.

@bizmureefa1921
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I just ask a random question I know the answer to two times to the same alien. So I (in the best case) know whether they are telling always the truth, are always lying or answer randomly. Then I ask the same alien if another one is Eff for example. So I know whether the answer is true or false. If it is the randomly-alien I need to use my luck I guess😂

@fcksaltwater
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Question 1 can't identify if an alien is Arr reliably. There's a 50% chance it can & a 50% chance it would not.

@StoneWinds
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so you can figure things out without understanding which is yes or no

@slimen3584
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I gave it a shot, best I could do is identify them with 5 questions. There is one insight that i got after trying to express the problem in a more mathematical way. There are 3!=6 possible permutations for the positions of the overlords and there are 2 choices regarding ulu=yes or ulu=no. This gives us a total of 6*2=12 possible worlds. we have 3 yes/no questions which corresponds to 3 bits of information (at best). This gives us the ability to reduce the search space to just 12 / 8 = 1.5 worlds. So it is impossible to consistently be able to identify the exact world with 3 questions. So it makes sense that in the solution, we cant tell whether ulu means yes or no, after we use our 3 questions.

@angelosefstratiou5352
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I figured out a sort of solution for the first part, but that’s still pretty good.

1. Does “Ozo” mean no? Only correct answer would be Ulu. If they answer “Ozo” It would create a paradox. Ex. (“Does no mean no?” “No.” Or “Does yes mean no?” “Yes”) If they answer Ulu, I’ll know I’m not talking to Eff, so we have one of them. Same if they answer Ozo, I’ll know I’m not talking to Tee. I’ll ask this to 2 of them separately If they both answer Ulu, I’ll know that the one I did not ask it to is Eff. If they both answer Ozo, I’ll know the one I’m not talking to is Tee. The Problem comes when they answer differently. I got stuck here but I’m proud that I figured that much out

@Whistlechip
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or you could just shuffle the artifacts between all three aliens until all of them are satisfied

@bettercallsly
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Absolutely fantastic riddle, potentially the best one out there. Its not just super easy, or just math in disguise. Truly, a complex yet logic based puzzle with a satisfying answer.

@PsychoTherapist-qv5pw
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now i can confidently say that not everything suits everyone

@geeksforthv
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No, TED-Ed, I can not solve the hardest logic puzzle ever.

@TechnoMax-v1g
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Question 1. Do you tell lies? The odd one out is rando who says yes, the other two will answer no. If all 3 say no then just repeat the question. The odd one out is Rando and the odd word out means yes.
Question 2. Does Rando tell lies? T answers yes, Rando answers yes but F answers No. Once again just repeat the question if required.

Two questions and we know both the identity of the Gods and the meaning of their yes and no words. Much simpler method than the video one.

@Nathan-dk8zz
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how are we supposed to know these aliens can understand human math?

@sleepneedsme827
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The ultimate problem of the solution for this puzzle is, it relies on a meta-assumption. Not rigorous. Feel free to ask why.

@cattkieu
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i ask one if he is tee, he responds "ulu" i ask another id he is eff, he responds "ozo" and i ask the last one if he is eff, he responds "ulu" and than im screwed.

@MrFrog-g3l
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...can't you say "if 'ulo' is incorrect and ozo is correct am i a human?" if the answer is ozo so correct/yes; and so it is either telling the truth or random (or liar or radom in case it said ulo). ask it again the same question and if it changes then it is arr. if it does not then it is tee (or in case it said ulo then eff) since it is telling the truth. if the first was telling the truth then ask it if thhe other alien is arr if it says no/ulo then it is eff and the last is arr. if it is the liar ask if the next one is the random is it answers olo then it is infact ozo. and finally if the first one was random take another alien and ask again "if 'ulo' is no and ozo is yes am i a human?" if it says ulo then liar if it says ozo then truthh.

@Jihanessa989
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I had to watch this 4 times to actually understand the solution

@mickisgamingsopleasewatch
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the real last question you can ask is what does ozo and ulu mean to tee, but I'm sure the alien overlords would get surprised

@AlexMukhamedyarov
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But when you know which is Tee, then you ask him is 1 + 1 = 2 ? If he say ozo or ulu, then you know which means yes and which means no.

@leeguan-wei1471
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so... you deciphered the entire language but not yes and no?? ok...

@AserGaming
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been trying to figure this riddle out without watching the full vid. Are we supposed to know which artifact is which, like the yellow one is the liars artifact. Or do we not know that either.

@The_Apollo_Showw
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>confirm that I have green eyes
>ask the aliens to leave

@TheGlacielSentinel
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Dog looks like he's nodebleeding

@I_them_vids_lol
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ask Tee if Eff tells the truth, Tee will say NO wether its ozo or ulu now you know which one means no.

@alexdjajic9604
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Spent 3 h with friends on this!!!!! WHY did this popped up at the end!!!!!! Arguably we SHOULD know the answer!!!!! Who can help us!!!!!! It's driving us CRAZY!!!! plz!!!! 4:32

@SophieX-v2t
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0:27 THE FIRE RISES

@Vesperstel
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4:07 table breakdown would really help

@ZekeDanielLai
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I CAN understand it, I just need some paper to write it down

@PatExMachina-ql6rn
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That’s an unbelievably twisted way to get there, and I’m not even sure it works lol. This is the way I solved it:

To find out what ozo and ulu mean, my first question was “are you the one who always lies?”, two of them will answer the word for “no” (both the one who’s lying and the one who always tells the truth), therefore there will be at least two people saying either ozo or ulu, that word is no.

Now that I know the meaning of ozo and ulu, I’ll ask a simple question to identify at least one alien. Is the Sky blue (or yellow in this case, lol)? Lying one will say no, truthful one will say yes, the random one will say either yes or no, meaning that two aliens will give the same answer and the one who gives a different answer is either the one who’s lying or the one who’s telling the truth (and I know which one because I know what ozo and ulu mean and I know the answer to my question).

Now, I can ask the one I know whether the alien next to him is the random one. Since I know if he’s lying or not, I will know whether the other alien is the random one or not. The remaining alien is obviously the other one.

@indigobuntz3564
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Alternative solution:
It’s a yes/no question, but the answer doesn’t have to be “yes” or “no”. You understand the rest of the language including, presumably, “I don’t know”.

You could ask one of them, “If I asked the other two if they were Eff, what would they say?”. If you get lucky and have asked it to Tee, the answer has to be, “I don’t know”, since he is bound to tell the truth, and he knows what Eff would say, but can’t say for sure what Arr would say. That confirms it’s Tee you’re talking to and one more question solves it: “Would this one say ozo if I asked them if they are Eff?”. “I don’t know” means you’re talking about Arr, “ozo” or “ulu” - doesn’t really matter which - means you’re talking about Eff. In just two questions you can identify two of them and therefore infer the third.

If you happen to get one of the others on the first question, you’ll hear either “ozo” or “ulu” - Arr randomly says either and Eff always lies so can’t say “I don’t know” - so you move on to the next and ask the same question again. “I don’t know” means you’ve found Tee and one more question (making it three in total) as above solves the problem.

If you move on to the next and both have answered any combination of “ozo” or “ulu” then you know that the third one must be Tee. For the third question, ask Tee what one of the others would say: “I don’t know” or “ozo/ulu” determines which one that is and so, by inference, which the other is.

@Crall-xb8he
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But how do I know what artifact the liar wants?

@narcissisticcapitalist443
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The animation is insanely cute omg

@drawn_by_starla9462
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OMG IT TOOK ME 2 HOURS AND 2 PAGES OF PAPERS WASTED JUST TO UNDERSTAND THIS....

@ExpiredSass