TEDTED-EdTED EdTED EducationAlex GendlerArtrake Studioriddleproblem solvingcritical thinkingRaymond SmullyanGeorge Boolos

View full lesson: http://ed.ted.com/lessons/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.

## Laura Clark

Q1: Would Arr say [ozo/ulu] to "does 2+2=4?" Only Arr knows, Tee and Eff will respond "I don't know" or "I definitely know" in order to accurately be truthful/lie respectively, while Arr would answer "ozo" or "ulu". With this question, you have determined the identity of one overlord.

Q2: Same thing, but to a different overlord. Now just use process of elimination, and done!

## yugijak

The biggest issue is that one answers randomly. You cannot be sure which one is the random answering one. So...

I think there needs to be 1 question that you can outright tell the correct answer two. It doesn't have to be 2+2=4 but it has to be something immediately able to have a correct and incorrect answer of true and false respectively.

The trick is largely eliminating 1 alien outright. You cannot ask them all 1 question at the same time which would help expose the randomly answering one.

Here's my thought: Take 1 alien. Ask them the following question twice: Are there three alien overlords? The Random answering alien...Arr...cannot answer the same way twice. If he did his answer would not be random, but consistent. Arr has to change his answer every time for it to be a random answer. Thus, if the alien answers the same way twice, it is not Arr but Tee or Eff. If he does not answer the same way twice, then it is Arr. Then take either of the other two aliens and ask them the same question. Eff will answer false, and Tee with answer true, leaving the leftover alien as whoever did not speak.

I'm probably wrong but...that's my theory. Time to see if I was right.

## ninjakiwirules

## Ethan Butler

## JJ_12

Regardless of the alien's order, we have 3 objectives:

1. determine which alien is r.

2. Determine which word is the negative.

3. Determine who is who between t and f.

The key question we are going to use (and slightly vary depending on responses) is "Would the alien in the position next to you say 2+2=4?" There are 3 different responses to this. R would say either positive or negative, since he is random. If you ask the question to t or f and their counterpart is in the next position, both of them will answer negatively, since t will be truthful and say f would not say 2+2=4, and f would lie and say t would not say 2+2=4. If you ask the question to t or f and r is next to them, there will be no response, since t ALWAYS tells the truth and f ALWAYS lies. Since they don't know what r will say, the only way not to break their rules is to not give a response.

With that understanding, let's take a scenario where the alien in position 1 is r. You ask "Would the alien in position 2 say 2+2=4?" You receive uzu or olo. Since there was a response, you can rule out the alien in position 2 being r, but the alien in position 1 might still be r. Moving to the second, you ask "Would the alien in position 3 say 2+2=4?" You receive either uzu or olo, which means that the final alien is not r, which means the first alien is r. You also know that the response you just received means no, due to the logic I presented in the above paragraph. The only step you have to do now is ask the same alien "does 2+2=4?" If the alien responds with the negative value you just learned, you know f is in position two and t in position 3. Conversely, if the alien responds with positive, you know the opposite is true

Now let's take a scenario where r is in the middle. You ask the alien in position 1 "Would the alien in position 2 say 2+2=4?" You don't receive an answer, so you know that 2 is r. Now you ask the alien in position 1 again "Would the alien in position 3 say 2+2=4?" Again, you know the answer is the equivalent of "no". So you ask alien 1 again "does 2+2=4?" If the answer is the same as the negative you just learned, position 1 is f and 3 is t, and vice-versa for a positive answer.

And now the final scenario where r is at the end. You ask the alien in position 1 "Would the alien in position 2 say 2+2=4?" You receive either uzu or olo. Since there was a response, you can rule out the alien in position 2 being r, but the alien in position 1 might still be r. Moving to the second, you ask "Would the alien in position 3 say 2+2=4? " You don't receive a response, which lets you know that the alien in position 3 is r, and that the response that the alien in position 1 gave is the equivalent to "no". Now ask the second alien "does 2+2=4?" if the alien answers with the negative, you know that 1 is t and 2 is f, and opposite for a positive answer.

So, there's my solution. You still figure out which each alien is, AND you get to find out which value is the negative and by elimination which is the positive.

## Jkayppobox

## Jkayppobox

## ClarkPlays ROBLOX

"If 'Yes' means Ozo, will you say Ozo?"

## Andy Zachel

## Boy Drop out

## Right Dude Here

## Luna Mint

## SENER ELTI

## youssef mhamed

## red cat

If 2+2=4 and ozo =yes. Then if you ask the liar god ,"If I ask you whether 2+2=4 true will you say ozo" then he will say ulu instead of ozo.

Thats a mistake. Or I am wrong?

## ri bin

even people (including me) who have the logic courses took times to understand the logic

## Litsky Pancakes

## Erin Lastname

## Idanos Styles

## sequoia perez

## Mimi Nguyen

## Shaydabop

## :Pinecone

## 민군주

## Annika van Putte

## Cosmedian Gamer

## HydesR01

## BritishLayerSandwich

## What Did You Do To My Drink

No

## Jacob Kim

## angelmushahf

## michael01123

## Bbear F

## Evan Blodgett

## Dory

## Lovely Shasi

## ThunderFox280 Original

Sooooooooooooo, technically, it's could be easier.

God I love loopholes.

## Wolffangdestiny 376

## Aufar Rizqi

## 황금비

## Kelly Tan

## plain lazy

## TaylorMIA

## MartoSpidera Spidera

## The King

## unic beast

## Naufal Khiyarulloh

## king james488

## samuel Woodouse

2. did i crash land here? truther $ lier % if random responds % then we know who the truther is if the random says $ then we know who the lier is

3. ask if one of the odd two out is the truther or the lier depending on which you know and judge the knows response accordingly

get on my level TED-Ed ;)

## CJ Kim