[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.99,0:00:09.44,Default,,0000,0000,0000,,Created by logician Raymond Smullyan
Dialogue: 0,0:00:09.44,0:00:12.57,Default,,0000,0000,0000,,and popularized by his colleague\NGeorge Boolos,
Dialogue: 0,0:00:12.57,0:00:17.18,Default,,0000,0000,0000,,this riddle has been called the hardest\Nlogic puzzle ever.
Dialogue: 0,0:00:17.18,0:00:21.52,Default,,0000,0000,0000,,You and your team have crash-landed\Non an ancient planet.
Dialogue: 0,0:00:21.52,0:00:26.52,Default,,0000,0000,0000,,The only way off is to appease\Nits three alien overlords,
Dialogue: 0,0:00:26.52,0:00:29.06,Default,,0000,0000,0000,,Tee, Eff, and Arr,
Dialogue: 0,0:00:29.06,0:00:31.74,Default,,0000,0000,0000,,by giving them the correct artifacts.
Dialogue: 0,0:00:31.74,0:00:34.60,Default,,0000,0000,0000,,Unfortunately, you don't\Nknow who is who.
Dialogue: 0,0:00:34.60,0:00:39.19,Default,,0000,0000,0000,,From an inscription, you learn that you\Nmay ask three yes or no questions,
Dialogue: 0,0:00:39.19,0:00:42.27,Default,,0000,0000,0000,,each addressed to any one lord.
Dialogue: 0,0:00:42.27,0:00:44.75,Default,,0000,0000,0000,,Tee's answers are always true,
Dialogue: 0,0:00:44.75,0:00:46.78,Default,,0000,0000,0000,,Eff's are always false,
Dialogue: 0,0:00:46.78,0:00:50.33,Default,,0000,0000,0000,,and Arr's answer is random each time.
Dialogue: 0,0:00:50.33,0:00:51.77,Default,,0000,0000,0000,,But there's a problem.
Dialogue: 0,0:00:51.77,0:00:54.84,Default,,0000,0000,0000,,You've deciphered the language enough\Nto ask any question,
Dialogue: 0,0:00:54.84,0:00:59.93,Default,,0000,0000,0000,,but you don't know which of the two\Nwords 'ozo' and 'ulu' means yes
Dialogue: 0,0:00:59.93,0:01:01.63,Default,,0000,0000,0000,,and which means no.
Dialogue: 0,0:01:01.63,0:01:05.19,Default,,0000,0000,0000,,How can you still figure out \Nwhich alien is which?
Dialogue: 0,0:01:05.19,0:01:08.15,Default,,0000,0000,0000,,Pause here if you want \Nto figure it out for yourself!
Dialogue: 0,0:01:08.15,0:01:09.97,Default,,0000,0000,0000,,Answer in: 3
Dialogue: 0,0:01:09.97,0:01:11.45,Default,,0000,0000,0000,,2
Dialogue: 0,0:01:11.45,0:01:12.72,Default,,0000,0000,0000,,1
Dialogue: 0,0:01:12.72,0:01:17.23,Default,,0000,0000,0000,,At first, this puzzle seems not just hard,\Nbut downright impossible.
Dialogue: 0,0:01:17.23,0:01:18.80,Default,,0000,0000,0000,,What good is asking a question
Dialogue: 0,0:01:18.80,0:01:23.23,Default,,0000,0000,0000,,if you can neither understand the answer\Nnor know if it's true?
Dialogue: 0,0:01:23.23,0:01:24.92,Default,,0000,0000,0000,,But it can be done.
Dialogue: 0,0:01:24.92,0:01:27.60,Default,,0000,0000,0000,,The key is to carefully formulate\Nour questions
Dialogue: 0,0:01:27.60,0:01:31.30,Default,,0000,0000,0000,,so that any answer \Nyields useful information.
Dialogue: 0,0:01:31.30,0:01:35.83,Default,,0000,0000,0000,,First of all, we can get around\Nto not knowing what 'ozo' and 'ulu' mean
Dialogue: 0,0:01:35.83,0:01:39.58,Default,,0000,0000,0000,,by including the words themselves\Nin the questions,
Dialogue: 0,0:01:39.58,0:01:43.54,Default,,0000,0000,0000,,and secondly, if we load each question\Nwith a hypothetical condition,
Dialogue: 0,0:01:43.54,0:01:47.99,Default,,0000,0000,0000,,whether an alien is lying or not\Nwon't actually matter.
Dialogue: 0,0:01:47.99,0:01:49.56,Default,,0000,0000,0000,,To see how that could work,
Dialogue: 0,0:01:49.56,0:01:53.63,Default,,0000,0000,0000,,imagine our question\Nis whether two plus two is four.
Dialogue: 0,0:01:53.63,0:01:55.40,Default,,0000,0000,0000,,Instead of posing it directly,
Dialogue: 0,0:01:55.40,0:01:59.35,Default,,0000,0000,0000,,we say, "If I asked you whether\Ntwo plus two is four,
Dialogue: 0,0:01:59.35,0:02:01.54,Default,,0000,0000,0000,,would you answer 'ozo'?"
Dialogue: 0,0:02:01.54,0:02:04.62,Default,,0000,0000,0000,,If 'ozo' means yes \Nand the overlord is Tee,
Dialogue: 0,0:02:04.62,0:02:07.36,Default,,0000,0000,0000,,it truthfully replies, "ozo."
Dialogue: 0,0:02:07.36,0:02:09.29,Default,,0000,0000,0000,,But what if we ask Eff?
Dialogue: 0,0:02:09.29,0:02:13.46,Default,,0000,0000,0000,,Well, it would answer "ulu,"\Nor no to the embedded question,
Dialogue: 0,0:02:13.46,0:02:17.12,Default,,0000,0000,0000,,so it lies and replies 'ozo' instead.
Dialogue: 0,0:02:17.12,0:02:20.05,Default,,0000,0000,0000,,And if 'ozo' actually means no,
Dialogue: 0,0:02:20.05,0:02:23.59,Default,,0000,0000,0000,,then the answer to \Nour embedded question is 'ulu,'
Dialogue: 0,0:02:23.59,0:02:27.07,Default,,0000,0000,0000,,and both Tee and Eff still reply 'ozo,'
Dialogue: 0,0:02:27.07,0:02:29.11,Default,,0000,0000,0000,,each for their own reasons.
Dialogue: 0,0:02:29.11,0:02:31.18,Default,,0000,0000,0000,,If you're confused about why this works,
Dialogue: 0,0:02:31.18,0:02:33.61,Default,,0000,0000,0000,,the reason involves logical structure.
Dialogue: 0,0:02:33.61,0:02:38.64,Default,,0000,0000,0000,,A double positive and a double negative\Nboth result in a positive.
Dialogue: 0,0:02:38.64,0:02:43.32,Default,,0000,0000,0000,,Now, we can be sure that asking\Neither Tee or Eff a question put this way
Dialogue: 0,0:02:43.32,0:02:47.46,Default,,0000,0000,0000,,will yield 'ozo'\Nif the hypothetical question is true
Dialogue: 0,0:02:47.46,0:02:49.63,Default,,0000,0000,0000,,and 'ulu' if it's false
Dialogue: 0,0:02:49.63,0:02:53.02,Default,,0000,0000,0000,,regardless of what \Neach word actually means.
Dialogue: 0,0:02:53.02,0:02:56.62,Default,,0000,0000,0000,,Unfortunately, \Nthis doesn't help us with Arr.
Dialogue: 0,0:02:56.62,0:03:01.23,Default,,0000,0000,0000,,But don't worry, we can use our first\Nquestion to identify one alien lord
Dialogue: 0,0:03:01.23,0:03:03.77,Default,,0000,0000,0000,,that definitely isn't Arr.
Dialogue: 0,0:03:03.77,0:03:08.11,Default,,0000,0000,0000,,Then we can use the second to find out\Nwhether its Tee or Eff.
Dialogue: 0,0:03:08.11,0:03:09.37,Default,,0000,0000,0000,,And once we know that,
Dialogue: 0,0:03:09.37,0:03:12.96,Default,,0000,0000,0000,,we can ask it to identify \None of the others.
Dialogue: 0,0:03:12.96,0:03:14.73,Default,,0000,0000,0000,,So let's begin.
Dialogue: 0,0:03:14.73,0:03:16.45,Default,,0000,0000,0000,,Ask the alien in the middle,
Dialogue: 0,0:03:16.45,0:03:22.12,Default,,0000,0000,0000,,"If I asked you whether the overlord on\Nmy left is Arr, would you answer 'ozo'?"
Dialogue: 0,0:03:22.12,0:03:26.34,Default,,0000,0000,0000,,If the reply is 'ozo,' \Nthere are two possibilities.
Dialogue: 0,0:03:26.34,0:03:30.96,Default,,0000,0000,0000,,You could already be talking to Arr,\Nin which case the answer is meaningless.
Dialogue: 0,0:03:30.96,0:03:34.92,Default,,0000,0000,0000,,But otherwise, you're talking to either\NTee or Eff,
Dialogue: 0,0:03:34.92,0:03:36.19,Default,,0000,0000,0000,,and as we know,
Dialogue: 0,0:03:36.19,0:03:41.40,Default,,0000,0000,0000,,getting 'ozo' from either one means \Nyour hypothetical question was correct,
Dialogue: 0,0:03:41.40,0:03:44.71,Default,,0000,0000,0000,,and the left overlord is indeed Arr.
Dialogue: 0,0:03:44.71,0:03:49.46,Default,,0000,0000,0000,,Either way, you can be sure the alien\Non the right is not Arr.
Dialogue: 0,0:03:49.46,0:03:52.07,Default,,0000,0000,0000,,Similarly, if the answer is 'ulu,'
Dialogue: 0,0:03:52.07,0:03:55.66,Default,,0000,0000,0000,,then you know the alien \Non the left can't be Arr.
Dialogue: 0,0:03:55.66,0:04:00.03,Default,,0000,0000,0000,,Now go to the overlord you've determined\Nisn't Arr and ask,
Dialogue: 0,0:04:00.03,0:04:04.16,Default,,0000,0000,0000,,"If I asked 'are you Eff?' \Nwould you answer 'ozo'?"
Dialogue: 0,0:04:04.16,0:04:07.15,Default,,0000,0000,0000,,Since you don't have to worry about\Nthe random possibility,
Dialogue: 0,0:04:07.15,0:04:11.30,Default,,0000,0000,0000,,either answer will \Nestablish its identity.
Dialogue: 0,0:04:11.30,0:04:14.37,Default,,0000,0000,0000,,Now that you know whether its\Nanswers are true or false,
Dialogue: 0,0:04:14.37,0:04:19.47,Default,,0000,0000,0000,,ask the same alien whether the center\Noverlord is Arr.
Dialogue: 0,0:04:19.47,0:04:23.98,Default,,0000,0000,0000,,The process of elimination will identify\Nthe remaining one.
Dialogue: 0,0:04:23.98,0:04:26.85,Default,,0000,0000,0000,,The satisfied overlords help you\Nrepair your ship
Dialogue: 0,0:04:26.85,0:04:28.86,Default,,0000,0000,0000,,and you prepare for takeoff.
Dialogue: 0,0:04:28.86,0:04:33.47,Default,,0000,0000,0000,,Allowed one final question, you ask\NTee if it's a long way to Earth,
Dialogue: 0,0:04:33.47,0:04:36.39,Default,,0000,0000,0000,,and he answers "ozo."
Dialogue: 0,0:04:36.39,0:04:39.28,Default,,0000,0000,0000,,Too bad you still don't know \Nwhat that means.