Can you solve the three gods riddle? – Alex Gendler


Created by logician Raymond Smullyan and popularized by his colleague
George Boolos, this riddle has been called the hardest
logic puzzle ever. You and your team have crash-landed
on an ancient planet. The only way off is to appease
its three alien overlords, Tee, Eff, and Arr, by giving them the correct artifacts. Unfortunately, you don’t
know who is who. From an inscription, you learn that you
may ask three yes or no questions, each addressed to any one lord. Tee’s answers are always true, Eff’s are always false, and Arr’s answer is random each time. But there’s a problem. You’ve deciphered the language enough
to ask any question, but you don’t know which of the two
words ‘ozo’ and ‘ulu’ means yes and which means no. How can you still figure out
which alien is which? Pause here if you want
to figure it out for yourself! Answer in: 3 2 1 At first, this puzzle seems not just hard,
but downright impossible. What good is asking a question if you can neither understand the answer
nor know if it’s true? But it can be done. The key is to carefully formulate
our questions so that any answer
yields useful information. First of all, we can get around
to not knowing what ‘ozo’ and ‘ulu’ mean by including the words themselves
in the questions, and secondly, if we load each question
with a hypothetical condition, whether an alien is lying or not
won’t actually matter. To see how that could work, imagine our question
is whether two plus two is four. Instead of posing it directly, we say, “If I asked you whether
two plus two is four, would you answer ‘ozo’?” If ‘ozo’ means yes
and the overlord is Tee, it truthfully replies, “ozo.” But what if we ask Eff? Well, it would answer “ulu,”
or no to the embedded question, so it lies and replies ‘ozo’ instead. And if ‘ozo’ actually means no, then the answer to
our embedded question is ‘ulu,’ and both Tee and Eff still reply ‘ozo,’ each for their own reasons. If you’re confused about why this works, the reason involves logical structure. A double positive and a double negative
both result in a positive. Now, we can be sure that asking
either Tee or Eff a question put this way will yield ‘ozo’
if the hypothetical question is true and ‘ulu’ if it’s false regardless of what
each word actually means. Unfortunately,
this doesn’t help us with Arr. But don’t worry, we can use our first
question to identify one alien lord that definitely isn’t Arr. Then we can use the second to find out
whether its Tee or Eff. And once we know that, we can ask it to identify
one of the others. So let’s begin. Ask the alien in the middle, “If I asked you whether the overlord on
my left is Arr, would you answer ‘ozo’?” If the reply is ‘ozo,’
there are two possibilities. You could already be talking to Arr,
in which case the answer is meaningless. But otherwise, you’re talking to either
Tee or Eff, and as we know, getting ‘ozo’ from either one means
your hypothetical question was correct, and the left overlord is indeed Arr. Either way, you can be sure the alien
on the right is not Arr. Similarly, if the answer is ‘ulu,’ then you know the alien
on the left can’t be Arr. Now go to the overlord you’ve determined
isn’t Arr and ask, “If I asked ‘are you Eff?’
would you answer ‘ozo’?” Since you don’t have to worry about
the random possibility, either answer will
establish its identity. Now that you know whether its
answers are true or false, ask the same alien whether the center
overlord is Arr. The process of elimination will identify
the remaining one. The satisfied overlords help you
repair your ship and you prepare for takeoff. Allowed one final question, you ask
Tee if it’s a long way to Earth, and he answers “ozo.” Too bad you still don’t know
what that means.

100 thoughts on “Can you solve the three gods riddle? – Alex Gendler

  1. If I asked you, "Is it a long way to Earth?"; would you answer OZO?

    You still don't know what OZO means, but you do know the answer to your question, at least!😉

  2. They never bothered to explain what to do in the case that Arr is the alien you spoke to when you asked your first question.

  3. ASK TWO QUESTIONS TO EACH OF THEM IN THE SAME MANNER:
    Q.1. ARE YOU ARR…?
    Q.2. ARE YOU TEE…?

    IF OZO=YES…..

    THE ANSWERS WOULD BE:

    | ARR | TEE | EFF |
    Q.1.| ∆ | ULU | OZO |
    Q.2.| ∆ | OZO | OZO |
    ∆= RANDOM ANSWER
    IF ANSWERS BY ARR MATCH EXACTLY TO THOSE BY TEE OR EFF……. WE WOULD STILL KNOW WHO THE OTHER ONE IS….BY SEEING THE TRENDS IN THE ANSWERS…….
    THE TRENDS ARE….
    1. EFF ANSWERS BOTH QUESTIONS THE SAME WAY. BOTH BEING YES.
    2. TEE ANSWERS THE QUESTIONS DIFFERENTLY. THE FIRST BEING NO.

    THAT WAY RECOGNIZING TEE OR EFF AND ALSO WHAT OZO AND ULU ACTUALLY MEAN.
    THEN WITH THE THIRD QUESTION STILL LEFT WITH US WE CAN KNOW THE POSITIONS OF THE LAST TWO.

    IF WE IDENTIFY TEE THEN WE KNOW HIS FIRST ANSWER WOULD BE NO

    IRRESPECTIVE OF WHAT OZO AND ULU MEAN WE WOULD DERIVE THEIR MEANINGS AND USING THE CHARTS AND THE TWO QUESTIONS WE WILL IDENTIFY THEM ALL….

    TED-ED PLEASE CRITIQUE MY ANSWER…..IS IT CORRECT OR NOT…?

  4. Arr is easy..than you ask both of them if they're Arr. They're going to say "no" so you will know which word is no. Then ask Tee and Eff if they are Tee/Eff.

  5. I have an alternate method :
    I would ask any one of them does ozo mean yes (if it does and i am asking tee) he would say ozo to me back, now if ozo means no and i am asking tee he would again say ozo
    So, if you ask tee :does ozo/ulu mean yes he would say ozo/ulu (he would repeat the word)
    But what if i am asking EEF?
    (If ozo means yes in this case)
    If i ask him does ozo mean yes?
    In this case he would say ulu

    So now truthfull guy reapeats the word back and lying guy says the other word (either ulu or ozo)

    Now i could go up to an alien and ask the question too only two of them and i would know who is who.

  6. Please… Please I am crying. How I can determinate which answer is ipoteticaly true or false? I don't know if they meens yes or no! How does could this be?!!
    Please I need answer. It's too much

  7. I thought we only got three questions, that’s where I’m stumped. And what if you’re talking to Arr with your hypothetical question?

  8. Ask if you a boy/ girl and you say it to two aliens and you get the truth and the random one if you're a boy/girl the fist one if it's the truth one it will say ozo or the other word and then you ask the other one( this is for the Random one) multiple times and if it says different answers it's random then the others if the truth and the random one answer the same thing then the other is the false one

    Well got this wrong

  9. I don't get step 2…. you know the God on the left isn't randomly, but you told it yourself both remaining gods will answerd a possitive answerd. ( + + = +, – – = + ) so how do you know this god shoul'd be either trueth or false? If someone knows please let me know??

  10. But have you considered whether the 3 aliens has the knowledge to answer the questions in the first place?
    And even if they do, how can you not know what ‘yes’ or ‘no’ in the alien language if you know that one of them means yes and the other means no?

    Besides, a guy in a hat always tell lies
    OZO 👎🏻| OWO 👍🏻 ULU 👎🏻| UWU 👍🏻

  11. ted ed's answer is just about knowing the meaning of oso and olo not about knowing their names
    i still dont understand the correct answer

  12. If you ask "Is 2+2=4" TEE would say ozo(yes) ans EFF would say ulu(no) and not ozo too, so your explanation makes no sense!!

  13. But then how do you know to ask yes-or-no questions? Surely the engraving wasn't in english.
    In that case I'll just ask ozo-or-ulu questions.

  14. Why cant we just hand over all the artifacts to one alien and say, "If it belongs to you, take it otherwise pass it on."?

  15. If you can speak words like “what” and “extremity” in that language how the frick can’t you say yes or no

  16. Both (as in eff and Teff) have their own reasons for saying let’s say “no” which prove that the hypothetical question is true. Just don’t combine them together if that makes sense. Or just pretend ur talking to only one of them and the other doesn’t exist. So let’s pretend we’re only asking the one who says truth , “If I were to ask you whether 2+2=4, would you say no?” The one who says truth would say, “No, I would not say no as I would say yes to that question (2+2=4)” Then that basically means by saying no, the one that says truth is essentially saying that 2+2 is 4 (REMEMBER pretend that there’s only the one who says truth in the room). And if you were to ask that question to the one that lies, he would think: as I am the liar I would say that 2+2 doesn’t equal to 4 as that is a true statement, but because I would say no to 2+2=4, when given the question on whether I would say no to that question, the true statement is yes, so I have to lie and say no. (REMEMBER just pretend that in this moment, there’s only the one who says false stuff in the room, because if there is only one who says false stuff in front of you, by replying no, and following his train of thought, we know that he’s saying 2+2 does equal to 4. ) Therefore it doesn’t actually matter who we ask cause both of them have their own reasons and train of thought that prove that by saying no, 2+2 is indeed 4.

  17. But what if the alien in the middle is Arr? This solution seems to work only if you assume that the alien in the middle is either Tee or Eff. It's a 2/3 shot, but not a certainty.

  18. This video only addresses half the riddle. You still don't know what artifact to give to what overlord. Maybe the artifacts are labeled and that wasn't mentioned is all I can think.

  19. “If I asked you if you are Eff, would you answer Ozo?”
    Monster says Ozo, is Eff
    Or
    Monster says Ulu, Is Tee
    “Is it a long way back to Earth?” Tee says Ozo
    “Too bad you still don’t know what Ozo means”

    Bruh, you pretty much revealed what Ozo meant

  20. Why not ask a math question like is 1+1 2 if tee who always tells the truth will say yes in alien language then you will know which one is yes in alien language and know whick is know in alien language see my idea is to go up to tee and ask him or her or it whats 1+1 then when he or her or it will tell you ulu or ozo either way then you will know what ulu means and ozo means

  21. Why don’t you just ask if ozo means yes. If they reply ozo, then ozo means yes. If they reply ulu, then ozo means no. Boom you know what they mean now 💥

    Jk that won’t work

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