TedTest

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

Unscramble the Blue Letters

Created by lcgioain Raymond Smullyan and popularized by his cloleague gergoe Boolos, this rdidle has been called the hdrseat 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 gniivg 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 pborelm. 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 manes no. How can you still figure out which alien is which? Pause here if you want to figure it out for yourself! aswner in: 3 2 1 At first, this puzzle seems not just hard, but downright impossible. What good is asking a qtiesuon if you can neither understand the answer nor know if it's true? But it can be done. The key is to carefully fatomrlue our qosneuits 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 cdonitoin, 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 asekd you whether two plus two is four, would you answer 'ozo'?" If 'ozo' means yes and the overlord is Tee, it tlfthuurly replies, "ozo." But what if we ask Eff? Well, it would answer "ulu," or no to the eedmebdd question, so it lies and rlieeps '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 reoasn involves logical surrtucte. 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 taknlig 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 alein 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 essablith its identity. Now that you know whether its answers are true or false, ask the same alien whether the cenetr overlord is Arr. The process of eiolmtnaiin will identify the remaining one. The saiitesfd 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.

Open Cloze

Created by ________ Raymond Smullyan and popularized by his _________ ______ Boolos, this ______ has been called the _______ 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 ______ 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 _______. 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 _____ no. How can you still figure out which alien is which? Pause here if you want to figure it out for yourself! ______ in: 3 2 1 At first, this puzzle seems not just hard, but downright impossible. What good is asking a ________ if you can neither understand the answer nor know if it's true? But it can be done. The key is to carefully _________ our _________ 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 _________, 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 _____ 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 ________ question, 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 confused about why this works, the ______ involves logical _________. 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 _______ 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 _____ 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 _________ its identity. Now that you know whether its answers are true or false, ask the same alien whether the ______ overlord is Arr. The process of ___________ will identify the remaining one. The _________ 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.

Solution

riddle
answer
satisfied
formulate
problem
logician
embedded
structure
reason
elimination
center
asked
establish
talking
hardest
condition
truthfully
george
replies
questions
question
means
colleague
alien
giving

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
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case
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establish
false
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george
giving
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hypothetical
identify
identity
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including
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meaningless
means
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overlords
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planet
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possibility
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problem
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question
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random
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repair
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reply
result
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satisfied
ship
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smullyan
structure
takeoff
talking
team
tee
time
true
truthfully
understand
word
words
work
works
worry
yield
yields