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Created by logician Raymond Smullyan

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and popularized by his colleague
George Boolos,

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this riddle has been called the hardest
logic puzzle ever.

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You and your team have crash-landed
on an ancient planet.

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The only way off is to appease
its three alien overlords,

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Tee, Eff, and Arr,

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by giving them the correct artifacts.

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Unfortunately, you don't
know who is who.

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From an inscription, you learn that you
may ask three yes or no questions,

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each addressed to any one lord.

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Tee's answers are always true,

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Eff's are always false,

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and Arr's answer is random each time.

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But there's a problem.

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You've deciphered the language enough
to ask any question,

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but you don't know which of the two
words 'ozo' and 'ulu' means yes

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and which means no.

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How can you still figure out 
which alien is which?

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Pause here if you want 
to figure it out for yourself!

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Answer in: 3

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2

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1

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At first, this puzzle seems not just hard,
but downright impossible.

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What good is asking a question

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if you can neither understand the answer
nor know if it's true?

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But it can be done.

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The key is to carefully formulate
our questions

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so that any answer 
yields useful information.

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First of all, we can get around
to not knowing what 'ozo' and 'ulu' mean

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by including the words themselves
in the questions,

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and secondly, if we load each question
with a hypothetical condition,

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whether an alien is lying or not
won't actually matter.

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To see how that could work,

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imagine our question
is whether two plus two is four.

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Instead of posing it directly,

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we say, "If I asked you whether
two plus two is four,

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would you answer 'ozo'?"

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If 'ozo' means yes 
and the overlord is Tee,

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it truthfully replies, "ozo."

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But what if we ask Eff?

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Well, it would answer "ulu,"
or no to the embedded question,

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so it lies and replies 'ozo' instead.

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And if 'ozo' actually means no,

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then the answer to 
our embedded question is 'ulu,'

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and both Tee and Eff still reply 'ozo,'

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each for their own reasons.

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If you're confused about why this works,

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the reason involves logical structure.

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A double positive and a double negative
both result in a positive.

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Now, we can be sure that asking
either Tee or Eff a question put this way

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will yield 'ozo'
if the hypothetical question is true

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and 'ulu' if it's false

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regardless of what 
each word actually means.

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Unfortunately, 
this doesn't help us with Arr.

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But don't worry, we can use our first
question to identify one alien lord

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that definitely isn't Arr.

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Then we can use the second to find out
whether its Tee or Eff.

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And once we know that,

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we can ask it to identify 
one of the others.

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So let's begin.

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Ask the alien in the middle,

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"If I asked you whether the overlord on
my left is Arr, would you answer 'ozo'?"

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If the reply is 'ozo,' 
there are two possibilities.

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You could already be talking to Arr,
in which case the answer is meaningless.

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But otherwise, you're talking to either
Tee or Eff,

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and as we know,

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getting 'ozo' from either one means 
your hypothetical question was correct,

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and the left overlord is indeed Arr.

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Either way, you can be sure the alien
on the right is not Arr.

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Similarly, if the answer is 'ulu,'

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then you know the alien 
on the left can't be Arr.

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Now go to the overlord you've determined
isn't Arr and ask,

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"If I asked 'are you Eff?' 
would you answer 'ozo'?"

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Since you don't have to worry about
the random possibility,

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either answer will 
establish its identity.

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Now that you know whether its
answers are true or false,

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ask the same alien whether the center
overlord is Arr.

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The process of elimination will identify
the remaining one.

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The satisfied overlords help you
repair your ship

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and you prepare for takeoff.

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Allowed one final question, you ask
Tee if it's a long way to Earth,

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and he answers "ozo."

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Too bad you still don't know 
what that means.