TedTest

From the Ted Talk by Alex Gendler: Can you solve the three gods riddle?

Unscramble the Blue Letters

Created by logician Raymond slyaumln and popularized by his colleague George Boolos, this riddle has been called the hardest ligoc puzzle ever. You and your team have crash-landed on an ancient planet. The only way off is to aaseppe its three alien overlords, Tee, Eff, and Arr, by giving them the correct artifacts. Unfortunately, you don't know who is who. From an ipcotsriinn, you laren 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 awesnr is random each time. But there's a problem. You've derehiepcd 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? puase here if you want to fugrie 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 yldies useful information. First of all, we can get around to not knowing what 'ozo' and 'ulu' mean by incdnluig the words themselves in the questions, and secondly, if we load each question with a hypothetical condition, whether an alien is liyng 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 trtlhfuuly replies, "ozo." But what if we ask Eff? Well, it would answer "ulu," or no to the embedded qitsouen, so it lies and rpieles '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 cunseofd about why this works, the reason involves logical structure. A double positive and a dluboe 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 mneas. Unfortunately, this doesn't help us with Arr. But don't wrroy, 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 mdldie, "If I asked you whether the overlord on my left is Arr, would you answer 'ozo'?" If the rlpey 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 olrovred 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 dteeirenmd 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 rimnaieng 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 eatrh, and he answers "ozo." Too bad you still don't know what that means.

Open Cloze

Created by logician Raymond ________ and popularized by his colleague George Boolos, this riddle has been called the hardest _____ puzzle ever. You and your team have crash-landed on an ancient planet. The only way off is to _______ its three alien overlords, Tee, Eff, and Arr, by giving them the correct artifacts. Unfortunately, you don't know who is who. From an ___________, you _____ 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 ______ is random each time. But there's a problem. You've __________ 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? _____ here if you want to ______ 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 ______ useful information. First of all, we can get around to not knowing what 'ozo' and 'ulu' mean by _________ the words themselves in the questions, and secondly, if we load each question with a hypothetical condition, whether an alien is _____ 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 __________ replies, "ozo." But what if we ask Eff? Well, it would answer "ulu," or no to the embedded ________, so it lies and _______ '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 ________ about why this works, the reason involves logical structure. A double positive and a ______ 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 _____. Unfortunately, this doesn't help us with Arr. But don't _____, 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 ______, "If I asked you whether the overlord on my left is Arr, would you answer 'ozo'?" If the _____ 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 ________ 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 __________ 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 _________ 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 _____, and he answers "ozo." Too bad you still don't know what that means.

Solution

reply
confused
question
determined
overlord
lying
learn
worry
earth
double
middle
inscription
remaining
appease
answer
figure
smullyan
yields
truthfully
logic
pause
deciphered
replies
means
including

Original Text

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.

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
hypothetical question	2

Important Words

addressed
alien
allowed
ancient
answer
answers
appease
arr
artifacts
asked
bad
boolos
called
carefully
case
center
colleague
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double
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earth
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elimination
embedded
establish
false
figure
final
find
formulate
george
giving
good
hard
hardest
hypothetical
identify
identity
imagine
impossible
including
information
inscription
involves
key
knowing
language
learn
left
lies
load
logic
logical
logician
long
lord
lying
matter
meaningless
means
middle
negative
overlord
overlords
pause
planet
popularized
posing
positive
possibilities
possibility
prepare
problem
process
put
puzzle
question
questions
random
raymond
reason
reasons
remaining
repair
replies
reply
result
riddle
satisfied
ship
similarly
smullyan
structure
takeoff
talking
team
tee
time
true
truthfully
understand
word
words
work
works
worry
yield
yields