0:00:06.994,0:00:09.445
Created by logician Raymond Smullyan

0:00:09.445,0:00:12.566
and popularized by his colleague[br]George Boolos,

0:00:12.566,0:00:17.176
this riddle has been called the hardest[br]logic puzzle ever.

0:00:17.176,0:00:21.515
You and your team have crash-landed[br]on an ancient planet.

0:00:21.515,0:00:26.516
The only way off is to appease[br]its three alien overlords,

0:00:26.516,0:00:29.056
Tee, Eff, and Arr,

0:00:29.056,0:00:31.745
by giving them the correct artifacts.

0:00:31.745,0:00:34.596
Unfortunately, you don't[br]know who is who.

0:00:34.596,0:00:39.187
From an inscription, you learn that you[br]may ask three yes or no questions,

0:00:39.187,0:00:42.266
each addressed to any one lord.

0:00:42.266,0:00:44.747
Tee's answers are always true,

0:00:44.747,0:00:46.776
Eff's are always false,

0:00:46.776,0:00:50.327
and Arr's answer is random each time.

0:00:50.327,0:00:51.767
But there's a problem.

0:00:51.767,0:00:54.839
You've deciphered the language enough[br]to ask any question,

0:00:54.839,0:00:59.927
but you don't know which of the two[br]words 'ozo' and 'ulu' means yes

0:00:59.927,0:01:01.628
and which means no.

0:01:01.628,0:01:05.188
How can you still figure out [br]which alien is which?

0:01:05.188,0:01:08.147
Pause here if you want [br]to figure it out for yourself!

0:01:08.147,0:01:09.968
Answer in: 3

0:01:09.968,0:01:11.447
2

0:01:11.447,0:01:12.716
1

0:01:12.716,0:01:17.228
At first, this puzzle seems not just hard,[br]but downright impossible.

0:01:17.228,0:01:18.797
What good is asking a question

0:01:18.797,0:01:23.227
if you can neither understand the answer[br]nor know if it's true?

0:01:23.227,0:01:24.918
But it can be done.

0:01:24.918,0:01:27.598
The key is to carefully formulate[br]our questions

0:01:27.598,0:01:31.298
so that any answer [br]yields useful information.

0:01:31.298,0:01:35.827
First of all, we can get around[br]to not knowing what 'ozo' and 'ulu' mean

0:01:35.827,0:01:39.578
by including the words themselves[br]in the questions,

0:01:39.578,0:01:43.539
and secondly, if we load each question[br]with a hypothetical condition,

0:01:43.539,0:01:47.988
whether an alien is lying or not[br]won't actually matter.

0:01:47.988,0:01:49.559
To see how that could work,

0:01:49.559,0:01:53.630
imagine our question[br]is whether two plus two is four.

0:01:53.630,0:01:55.399
Instead of posing it directly,

0:01:55.399,0:01:59.348
we say, "If I asked you whether[br]two plus two is four,

0:01:59.348,0:02:01.539
would you answer 'ozo'?"

0:02:01.539,0:02:04.619
If 'ozo' means yes [br]and the overlord is Tee,

0:02:04.619,0:02:07.359
it truthfully replies, "ozo."

0:02:07.359,0:02:09.289
But what if we ask Eff?

0:02:09.289,0:02:13.459
Well, it would answer "ulu,"[br]or no to the embedded question,

0:02:13.459,0:02:17.116
so it lies and replies 'ozo' instead.

0:02:17.116,0:02:20.049
And if 'ozo' actually means no,

0:02:20.049,0:02:23.589
then the answer to [br]our embedded question is 'ulu,'

0:02:23.589,0:02:27.069
and both Tee and Eff still reply 'ozo,'

0:02:27.069,0:02:29.110
each for their own reasons.

0:02:29.110,0:02:31.180
If you're confused about why this works,

0:02:31.180,0:02:33.610
the reason involves logical structure.

0:02:33.610,0:02:38.640
A double positive and a double negative[br]both result in a positive.

0:02:38.640,0:02:43.320
Now, we can be sure that asking[br]either Tee or Eff a question put this way

0:02:43.320,0:02:47.461
will yield 'ozo'[br]if the hypothetical question is true

0:02:47.461,0:02:49.630
and 'ulu' if it's false

0:02:49.630,0:02:53.020
regardless of what [br]each word actually means.

0:02:53.020,0:02:56.621
Unfortunately, [br]this doesn't help us with Arr.

0:02:56.621,0:03:01.231
But don't worry, we can use our first[br]question to identify one alien lord

0:03:01.231,0:03:03.771
that definitely isn't Arr.

0:03:03.771,0:03:08.112
Then we can use the second to find out[br]whether its Tee or Eff.

0:03:08.112,0:03:09.371
And once we know that,

0:03:09.371,0:03:12.955
we can ask it to identify [br]one of the others.

0:03:12.955,0:03:14.732
So let's begin.

0:03:14.732,0:03:16.452
Ask the alien in the middle,

0:03:16.452,0:03:22.122
"If I asked you whether the overlord on[br]my left is Arr, would you answer 'ozo'?"

0:03:22.122,0:03:26.342
If the reply is 'ozo,' [br]there are two possibilities.

0:03:26.342,0:03:30.961
You could already be talking to Arr,[br]in which case the answer is meaningless.

0:03:30.961,0:03:34.921
But otherwise, you're talking to either[br]Tee or Eff,

0:03:34.921,0:03:36.191
and as we know,

0:03:36.191,0:03:41.402
getting 'ozo' from either one means [br]your hypothetical question was correct,

0:03:41.402,0:03:44.713
and the left overlord is indeed Arr.

0:03:44.713,0:03:49.463
Either way, you can be sure the alien[br]on the right is not Arr.

0:03:49.463,0:03:52.072
Similarly, if the answer is 'ulu,'

0:03:52.072,0:03:55.662
then you know the alien [br]on the left can't be Arr.

0:03:55.662,0:04:00.027
Now go to the overlord you've determined[br]isn't Arr and ask,

0:04:00.027,0:04:04.163
"If I asked 'are you Eff?' [br]would you answer 'ozo'?"

0:04:04.163,0:04:07.152
Since you don't have to worry about[br]the random possibility,

0:04:07.152,0:04:11.303
either answer will [br]establish its identity.

0:04:11.303,0:04:14.373
Now that you know whether its[br]answers are true or false,

0:04:14.373,0:04:19.471
ask the same alien whether the center[br]overlord is Arr.

0:04:19.471,0:04:23.984
The process of elimination will identify[br]the remaining one.

0:04:23.984,0:04:26.853
The satisfied overlords help you[br]repair your ship

0:04:26.853,0:04:28.863
and you prepare for takeoff.

0:04:28.863,0:04:33.473
Allowed one final question, you ask[br]Tee if it's a long way to Earth,

0:04:33.473,0:04:36.393
and he answers "ozo."

0:04:36.393,0:04:39.283
Too bad you still don't know [br]what that means.