Can you solve the three gods riddle? - Alex Gendler

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.

[AgentBurgo]

“You and your team have crash landed on a ancient planet”

Good to know my team consists of me and a dog

[Abi-hqlm]

"So.. can you solve the riddle?"
"Well ozo, but actually ulu"

[realmuha]

Me: So. How much complexity do you wanna put in a single 4-minutes video?
TED-Ed: Ozo.

[rmhz]

I couldn't understand it at first, but now that it has been explained i still can't

[ohheyimjulez]

Thank God we landed next to that rock engraved with the information we needed.

[adrijarambhatla]

Me: knows entire alien language
Also me: doesn't know the difference between yes and no

[candarus_collective]

I tried for HOURS to solve this and honestly I'm proud of myself for how much I figured out, even though I never got to the full solution

[CubicSagacity]

Long-winded breakdown of why you don't need to know the exact meaning of "OZO" and "ULU", and why Arr doesn't prevent a solution (the first part is pretty much a reiteration of the video, but at the end I try to explain my understanding of it):

Tee (T) tells the truth
Eff (F) tells a lie
Arr (R) answers randomly

Question: "If I asked you whether 2+2=4 (known true), would you say 'OZO' (unknown meaning)?"

IF "OZO" = "Yes" AND "ULU" = "No"

Answers:
T: "OZO"
F: "OZO" (He would say "ULU" to the embedded question, so he denies this and says "OZO".)

IF "ULU" = "Yes" AND "OZO" = "No"

Answers:
T: "OZO"
F: "OZO" (Yes, he would say "OZO" to the embedded question, so he denies this and says "OZO".)

Like this:
- Q to F: "Does 2+2=4?:
- F: "OZO"
- Q to F: "If I asked you whether 2+2=4, would you say 'OZO'?"
- F: "OZO" (Must lie about his previous answer and deny that he WOULD say "OZO", but because "OZO" means "No" in this example, he uses the word "OZO" in order to deny it.)

Question: "If I asked you whether 2+2=5 (known false), would you say 'OZO' (unknown meaning)?" (Assuming the year is not 1984)

IF "OZO" = "Yes" AND "ULU" = "No"

Answers:
T: "ULU"
F: "ULU"

IF "ULU" = "Yes" AND "OZO" = "No"

Answers:
T: "ULU"
F: "ULU"

Question: "If I asked you whether the overlord on my left is Arr (unknown), would you answer 'OZO' (unknown meaning)?"

IF "OZO" = "Yes" AND "ULU" = "No", AND Arr IS to the left

Answers:
T: "OZO"
F: "OZO"

IF "ULU" = "Yes" AND "OZO" = "No", AND Arr IS to the left

Answers:
T: "OZO"
F: "OZO"

IF "OZO" = "Yes" AND "ULU" = "No", AND Arr IS NOT to the left

Answers:
T: "ULU"
F: "ULU"

IF "ULU" = "Yes" AND "OZO" = "No", AND Arr IS NOT to the left

Answers:
T: "ULU"
F: "ULU"

~

So you aren't finding out the meaning of the words, but you ARE determining the validity of your embedded question.  You know that an answer of "OZO" from Tee or Eff means that the embedded question is true, and an answer of "ULU" from them means that the embedded question is false.

On to the matter of determining order.  Posed to the middle alien, the first question is this: "If I asked you whether the overlord on my left is Arr (unknown), would you answer 'OZO' (unknown meaning)?"

This question isn't about confirming who IS Arr, it's about confirming who IS NOT Arr.

If Arr is on either side, the first alien you're talking to must be Tee/Eff and you'd then know for sure where Arr is based on their answer.  If Arr is in the middle, then the answer he gives would still point you in the correct direction because he ISN'T on either side.  If Arr says "OZO" randomly, you would now be choosing between left and middle alien.  If Arr says "ULU" randomly, you would be choosing between right and middle alien.  Either way, you've determined the two spots where Arr COULD be and, more importantly, the one where he definitely COULDN'T be.

Originally, I was confused because it seemed like this solution required starting with Tee/Eff for sure, and already knowing which side Arr is on so you can formulate your question accordingly and know that you wouldn't be getting a random answer.  However, getting a random answer isn't as much of a wrench in the works as I first thought, because that in itself can be used to make an elimination as Arr can't be in two places at once.

I'm not claiming to be an expert logician or anything and I admit that I could definitely be wrong, but that's my understanding of this riddle.  In my opinion, the hardest part to understand is the fact that Arr answering randomly doesn't prevent you from being able to find the correct answer, so I decided to post how I worked through it in case it might be a help to anyone else.  :)

[ayushmehta]

TED-Ed: Did you solve the puzzle?
Me: Ozo.

[EkittyMonte]

So let me get this straight, you literally know EVERY single word in their language except for yes and no

[puppetgeneral]

I pick up an artifact at random and pretend to drop it. I watch as one of the overlord’s eyes widen. It’s his artifact.

I pick up another artifact and say “It’s chipped. See?” The first overlord to come forward does so in a worried rush. It’s his artifact.

The last one I toss to the last overlord and say goodbye.

[TheIndieGhost]

Just realized that the names of the gods are, in a way, what they do.
"Tee" sounds like T -> True
"Eff" sounds like F -> False
"Arr" sound like R -> Random

[fathomgaming]

“You and your team have crash landed on an ancient planet”

**9 year old girl and a dog walk out of the space ship**

[gamechep]

*Me* : If I asked you if Schrödinger's cat is alive, would you say OZO?
*Alien overlords* : * visible confusion *

[markimbing]

2:15 It would be better to explain this by not using ozo or ulu. For example: “If I asked you if 2+2=4, would you say yes?” To the embedded question, Tee would say yes. Tee would reply to your question and say “Yes, I would say yes if you asked me if 2+2=4.”
The rules state that Eff always lies. It doesn’t imply that Eff would say the opposite of Tee or vice versa. To the embedded question, Eff would say no. If he said “No, I would say no to 2+2=4.”, that means he said something true, which contradicts his rule of lying. Instead, he would lie and say “Yes, I would say yes to 2+2=4.”

Reverse example: “If I asked you if 2+2=4, would you say no?” To the embedded question, Tee would say no, so Tee replies and says “No, I would say yes to 2+2=4.” Eff, again, would tell the truth and break his lying rule if he says “Yes, I would say no to 2+2=4.” So he would have to say “No, I would say yes to 2+2=4.”

[dVTHoR]

I’m just happy to say, despite not coming up with the answer, I was finally able to completely
Understand the solution after some time. It took a while thought as they brush through that solution so fast without explaining in detail.

It’s pretty remarkable for someone to come up with the full answer. In hindsight, it makes so much sense that question 1 must isolate one that isn’t the random answerer - as no other questions can contain information until you have at least that. But still.. even making that discovery, coming up with that first question is very difficult to do.

[Nogha]

>this riddle has been called the hardest logic puzzle ever
>pause here if you want to figure it out for yourself!
Excuse me who do you think I am

[XEZ]

Little did you know, TEE helped to repair ship as he promised, EFF lied about fixing your ship and messed up your navigation system instead, while ARR left a timed bomb as a gift.

[electric_chris]

After seven years, I am proud to say that I finally understand the solution to this riddle (although I would still have no clue how to solve the riddle independently)

[jlyaaburnee]

an explanation;

the gist of this whole riddle is to emphasize the power of a double negative. we can obtain all the information we need from these gods using double negatives, without even knowing the meaning of the answer or the how truthful it is.

understanding why tee and eff will give their given answers is the easy part, at least when we are asking questions we know whether or not are true or false. i think when we try to get answers we dont already know, thats when it gets difficult and we get lost in the sauce.

instead of ozo and ulu, ill use x and y for simplicity, with ozo=x and ulu=y.

if the embedded question is true, no matter what x or y is, what we ask is going to either give a double positive or negative.

(if i ask you whether or not the sky is blue, would you answer x?)

when x=yes
tee —> x!
eff —> x! (to the question itself, it would answer y)

when x=no
tee —> x!
eff —> x! (lies about lying to the embedded question.)

the important part here is to realize they both responded x because the embedded question was true.
what would happen if it was false?

(if asked you whether or not the sky is red, would you answer x?)

when x=yes

tee —> y!
eff —> y! (would say x to embedded question)

when x=no

tee —> y!
eff —> y! (would say x to embedded question.)

the takeaway is _when our embedded question is true, _ irregardless of what x or y is, we will get that same variable we put in our question back from them. thats the only thing all that x and y mess above told us thats important.

now that we know what the answers to true and false questions look like, we can use the gods responses to see whether or not their responses match a true or false embedded statement. look;

if i asked you whether *abc, * would you answer x?

if a god responds —> x

then we have proved above that abc must be a true statement, and we learned something new!

if a god responds —> y

then we have proved that abc must be false. just scroll up!

now we use statements on the position of the gods to get them to sell each other out!

but do not lost sight of the big picture— we dont care what ozo and ulu are! we dont need to! it doesnt matter! what matters is _if your embedded question is true!_