Can you solve the three gods riddle? – Alex Gendler

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 to “Can you solve the three gods riddle? – Alex Gendler”

  1. If Arr answers randomly ("Arr's answers are random each time) and you ask Arr this question, what if he answers with "Schmerkle" or "Quanglock" or some other random possibility? This language has only one term for yes and no? Random only means random between positive and negative?

    It's not a HARD logic puzzle. It's a FLAWED logic puzzle.

  2. I can't understand the whole double positives and double negatives thing with the ozo and ulu scenario in the beginning. Here's my thought process:

    If ozo means yes, and ulu means no:
    if i were to ask you if 2+2=4, would you say ozo? Tee: ozo
    same question, would you say ulu? Tee: ulu
    same question, would you say ozo? Eff: ozo
    same question, would you say ulu? Eff: ulu

    If ozo means no, and ulu means yes:
    if i were to ask you if 2+2=4, would you say ozo? Tee: ozo
    same question, would you say ulu? Tee: ulu
    same question, would you say ozo? Eff: ozo
    same question, would you say ulu? Eff: yes

    They said that if the scenario were true, they'd both say ozo, and if it were false, they'd both say ulu. I only found that true when ozo meant yes.
    I know i'm wrong, I just don't understand why. What am I missing?

  3. whats the point of her asking them and solving a riddle if theres no problem….. also it makes no sense to ask that question because it could be that guy whos random…. bruh

  4. @ted-ed

    Love it, but after all the logic, it feels like you have made one mistake at the end of this video.
    Following the same logic as in the solution, Tee’s answer at the end would tell you, that it is indeed a long way to Earth. Disregarding the fact if OZO is yes or no.

  5. My solution:
    3 artifacts and 3 aliens. So total 6 possible combinations to distribute them randomly.
    Try any one of them and you have a 16.67% chance of getting it right. I like to gamble.

  6. OMG I UNDERSTOOD THE QUESTION WRONG AND I WAS TRYING TO FIND WHICH ARTIFACT BELONGED TO WHICH BY ASKING THE GODS INDIVIDUALLY i wasted 40 minutes

  7. Guys i found it out.
    To make it easy for you
    Tee Eff Arr
    Ok so You dont hv to guess the meaning of ozo and ulu. We only have to find tee or eff.
    First ask the aliens a generic question thats a fact. Like. "If we crashed here answer ozo" since tee answer fact and eff false we dont have to worry about arr. Heres why. If 2 numbers of monsters answer ozo and one is ulu. The one who answered the ulu is surely eff. But if theres 2 ulu and 1 ozo the ozo is surely tee. After this you know either tee or eff you need to determine arr.
    First scene is u found tee. Ask tee if arr is in the middle say ozo. If he say ulu then arr is in the right side as demonstrated on top. And when ozo in the middle is indeed arr. And eff is in the right.
    2nd scene is u found eff, ask eff if arr is in the middle say ozo. When eff say ozo arr is in the right side and when ulu its in the middle.
    And that took like 3 min of me thinking before watching the solution and after it took like 2 hrs lol

  8. Well, you always could ask him "if I asked you whether it is a long way to Earth would you say OZO?" If TEE replies OZO then it is, indeed, regardless of the meaning , whereas if he replied ULU then it wouldn't definitely. a) If OZO is YES, there you have your answer. b) If OZO was NO, no problem! "If I asked you whether it is a long way to Earth would you say OZO/NO? If he replied OZO/NO, then he would NOT be saying that the Earth is NOT far away, which is the same as saying that the Earth is actually far away. Now, if ULU is NO, and therefore OZO is YES, we are in situation a) again. However, If ULU meant YES, then OZO would mean NO and we'd be in situation b).

  9. I got the double negation thing quickly but still I didn't fully understand how could I know whether I'm talking to TEE or EFF. If the statement is true (2+2=4) both would agree in their answers. But if the statement is false (2+2=5) both would still agree. So, after thinking and writing down all my hypothesis, I came to the following outcome: the only way to identify one from the other is a disagreement in the answer. And you could find that disagreement by asking directly if they are one of the two. So, if the statement is (I AM TEE), TEE himself would answer OZO, whereas EFF would answer ULU (he would say OZO to make us think he is not him but TEE, however, because he's a liar, he would finally tell us that actually he wouldn't have answered OZO but ULU). Then, you can be sure it's TEE. Now, if the statement is (I AM EFF), TEE would tell us ULU, because he wouldn't find the statement as being correct, yet EFF would say OZO because he would lie to us again: If I asked you whether you are EFF, would you say OZO? In the first place he would say ULU to the statement so that he could be tricking us into thinking he isn't actually EFF (liar!) but since he would lie in his answer as well, he would tell us OZO (twice a liar! = true statement). So, once you have decided who can't definitely be ERR, you will find out the others' true identities through their disagreement. If the question is "If I asked you whether you are EFF would you say OZO?" and they said ULU, it's TEE talking whereas if they answered OZO, it's EFF himself lying in his statements on his hypothetical answers. And the other way around.

  10. If I were to ask one of the alien overlords: Do I have something in my left hand?

    The Honest one would not answer right? because he only answers Honestly.

    The Liar and Random, would answer Ozo or Ulu.

  11. Is this really the hardest riddle of all time? Just ask them what your name is these is a then you can guarentee who is lying but the random and right alien would say your name correctly also the random alien has a chance of ratting himself out then you have 2 more chances of cathing the random alien out

  12. My question woud be, "Hey Tee, are you an overlord?", the allien that answers would be Tee and whatever he answers would means yes, my second and last question would be, "Hey Eeef, are you an overlord?" the allien that answers would be Eef and whatever he answers woul mean no, and the other allien woud be Aarf, with no question for him. I addressed my questions to a specific allien, first one to Tee and second one to Eef and the answers have only yes or no answers

  13. I FINALLY GET IT. All this time i have been irritated at the supposed answer to the riddle because it neglects to address the issue of asking ARR a question and unknowingly getting a useless answer. BUT I GET IT NOW. ive always wrongfully assumed ARR gives a random answer, but he DOESN'T. HE RANDOMLY PICKS BETWEEN THE TRUTH OR A LIE. Either of which will grant the same answer. Thats the important distinction.

  14. If I can ask a question more than once .. can't I ask aar the same question multiple times and get different answers ..making the riddle easier….

  15. There’s a typo in the end! The bubble shows that’s it’s a hypothetical question but narrator asks a direct question.

  16. Ask any of them, "If I asked Arr a question, would they answer Ozo/Ulu?" (either one will work) if they are Tee or Eff, they wont be able to answer truthfully or falsely, as Arr's answers are always random, so if they answer, they are Arr. if not, they are Tee or Eff. Thats my first step, i dont really know were to go from there.

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