9:59:59.000,9:59:59.000
Created my logician Raymond Smullyan

9:59:59.000,9:59:59.000
and popularized by his colleague[br]Goerge Boolos,

9:59:59.000,9:59:59.000
this riddle has been called the hardest[br]logic puzzle ever.

9:59:59.000,9:59:59.000
You and your team have crash-landed[br]on an ancient planet.

9:59:59.000,9:59:59.000
The only way off is to appease[br]its three alien overloards,

9:59:59.000,9:59:59.000
Tee, Eff, and Arr,

9:59:59.000,9:59:59.000
by giving them the correct artifacts.

9:59:59.000,9:59:59.000
Unfortunately, you don't[br]know who is who.

9:59:59.000,9:59:59.000
From an inscription, you learn that you[br]may ask three yes or no questions,

9:59:59.000,9:59:59.000
each addressed to any one lord.

9:59:59.000,9:59:59.000
Tee's answers are always true,

9:59:59.000,9:59:59.000
Eff's are always false,

9:59:59.000,9:59:59.000
and Arr's answer is random each time.

9:59:59.000,9:59:59.000
But there's a problem.

9:59:59.000,9:59:59.000
You've deciphered the language enough[br]to ask any question,

9:59:59.000,9:59:59.000
but you don't know which of the two[br]words ozo and ulu means yes

9:59:59.000,9:59:59.000
and which means no.

9:59:59.000,9:59:59.000
How can you still figure out [br]which alien is which?

9:59:59.000,9:59:59.000
Pause here if you want [br]to figure it out for yourself!

9:59:59.000,9:59:59.000
Answer in: 3

9:59:59.000,9:59:59.000
2

9:59:59.000,9:59:59.000
1

9:59:59.000,9:59:59.000
At first, this puzzle seems not just hard,[br]but downright impossible.

9:59:59.000,9:59:59.000
What good is asking a question

9:59:59.000,9:59:59.000
if you can neither understand the answer[br]nor know if it's true?

9:59:59.000,9:59:59.000
But it can be done.

9:59:59.000,9:59:59.000
The key is to carefully formulate[br]our questions

9:59:59.000,9:59:59.000
so that any answer [br]yields useful information.

9:59:59.000,9:59:59.000
First of all, we can get around[br]to not knowing ozo and ulu mean

9:59:59.000,9:59:59.000
by including the words themselves[br]in the questions,

9:59:59.000,9:59:59.000
and secondly, if we load each question[br]with a hypothetical condition,

9:59:59.000,9:59:59.000
whether an alien is lying or not[br]won't actually matter.

9:59:59.000,9:59:59.000
To see how that could work,

9:59:59.000,9:59:59.000
imagine our questions[br]is whether two plus two is four.

9:59:59.000,9:59:59.000
Instead of posing it directly,

9:59:59.000,9:59:59.000
we say, "If I asked you whether[br]two plus two is four,

9:59:59.000,9:59:59.000
would you answer 'ozo'?"

9:59:59.000,9:59:59.000
If 'ozo' means yes [br]and the overlord is Tee,

9:59:59.000,9:59:59.000
it truthfully replies, "ozo."

9:59:59.000,9:59:59.000
But what if we ask Eff?

9:59:59.000,9:59:59.000
Well, it would answer "ulu,"[br]or no to the embedded question,

9:59:59.000,9:59:59.000
so it lies and replies ozo instead.

9:59:59.000,9:59:59.000
And if 'ozo' actually means no,

9:59:59.000,9:59:59.000
then the answer to [br]our embedded question is 'ulu,'

9:59:59.000,9:59:59.000
and both Tee and Eff still reply 'ozo,'

9:59:59.000,9:59:59.000
each for their own reasons.

9:59:59.000,9:59:59.000
If you're confused about why this works,

9:59:59.000,9:59:59.000
the reason involves logical structure.

9:59:59.000,9:59:59.000
A double positive and a double negative[br]both result in a positive.

9:59:59.000,9:59:59.000
Now, we can be sure that asking[br]either Tee or Eff a question put this way

9:59:59.000,9:59:59.000
will yield 'ozo'[br]if the hypothetical question is true

9:59:59.000,9:59:59.000
and 'ulu' if it's false

9:59:59.000,9:59:59.000
regardless of what [br]each word actually means.

9:59:59.000,9:59:59.000
Unfortunately, [br]this doesn't help us with Arr.

9:59:59.000,9:59:59.000
But don't worry, we can use our first[br]questions to identify one alien lord

9:59:59.000,9:59:59.000
that definitely isn't Arr.

9:59:59.000,9:59:59.000
Then we can use the second to find out[br]whether its Tee or Eff.

9:59:59.000,9:59:59.000
And once we know that,

9:59:59.000,9:59:59.000
we can ask it to identify [br]one of the others.

9:59:59.000,9:59:59.000
So let's begin.

9:59:59.000,9:59:59.000
Ask the alien in the middle,

9:59:59.000,9:59:59.000
"If I asked you whether the overlord on[br]my left is Arr, would you answer 'ozo'?"

9:59:59.000,9:59:59.000
If the reply is 'ozo,' [br]there are two possibilities.

9:59:59.000,9:59:59.000
You could already be talking to Arr,[br]in which case the answer is meaningless.

9:59:59.000,9:59:59.000
But otherwise, you're talking to either[br]Tee or Eff,

9:59:59.000,9:59:59.000
and as we know,

9:59:59.000,9:59:59.000
getting 'ozo' from either one means [br]you hypothetical question was correct,

9:59:59.000,9:59:59.000
and the left overlord is indeed Arr.

9:59:59.000,9:59:59.000
Either way, you can be sure the alien[br]on the right is not Arr.

9:59:59.000,9:59:59.000
Similarly, if the answer is 'ulu,'

9:59:59.000,9:59:59.000
then you know the alien [br]on the left can't be Arr.

9:59:59.000,9:59:59.000
Now go to the overlord you've determined[br]isn't Arr and ask,

9:59:59.000,9:59:59.000
"If I asked 'arr you Eff?' [br]would you answer 'ozo'?"

9:59:59.000,9:59:59.000
Since you don't have to worry about[br]the random possibility,

9:59:59.000,9:59:59.000
either answer will [br]establish its identity.

9:59:59.000,9:59:59.000
Now that you know whether its[br]answers are true or false,

9:59:59.000,9:59:59.000
ask the same alien whether the center[br]overlord is Arr.

9:59:59.000,9:59:59.000
The process of elimination will identify[br]the remaining one.

9:59:59.000,9:59:59.000
The satisfied overlords help you[br]repair your ship

9:59:59.000,9:59:59.000
and you prepare for takeoff.

9:59:59.000,9:59:59.000
Allowed one final question, you ask[br]Tee if it's a long way to Earth,

9:59:59.000,9:59:59.000
and he answers 'ozo.'

9:59:59.000,9:59:59.000
Too bad you still don't know [br]what that means.