Can you solve the three gods riddle? - Alex Gendler
-
0:07 - 0:09Created by logician Raymond Smullyan
-
0:09 - 0:13and popularized by his colleague
George Boolos, -
0:13 - 0:17this riddle has been called the hardest
logic puzzle ever. -
0:17 - 0:22You and your team have crash-landed
on an ancient planet. -
0:22 - 0:27The only way off is to appease
its three alien overlords, -
0:27 - 0:29Tee, Eff, and Arr,
-
0:29 - 0:32by giving them the correct artifacts.
-
0:32 - 0:35Unfortunately, you don't
know who is who. -
0:35 - 0:39From an inscription, you learn that you
may ask three yes or no questions, -
0:39 - 0:42each addressed to any one lord.
-
0:42 - 0:45Tee's answers are always true,
-
0:45 - 0:47Eff's are always false,
-
0:47 - 0:50and Arr's answer is random each time.
-
0:50 - 0:52But there's a problem.
-
0:52 - 0:55You've deciphered the language enough
to ask any question, -
0:55 - 1:00but you don't know which of the two
words 'ozo' and 'ulu' means yes -
1:00 - 1:02and which means no.
-
1:02 - 1:05How can you still figure out
which alien is which? -
1:05 - 1:08Pause here if you want
to figure it out for yourself! -
1:08 - 1:10Answer in: 3
-
1:10 - 1:112
-
1:11 - 1:131
-
1:13 - 1:17At first, this puzzle seems not just hard,
but downright impossible. -
1:17 - 1:19What good is asking a question
-
1:19 - 1:23if you can neither understand the answer
nor know if it's true? -
1:23 - 1:25But it can be done.
-
1:25 - 1:28The key is to carefully formulate
our questions -
1:28 - 1:31so that any answer
yields useful information. -
1:31 - 1:36First of all, we can get around
to not knowing what 'ozo' and 'ulu' mean -
1:36 - 1:40by including the words themselves
in the questions, -
1:40 - 1:44and secondly, if we load each question
with a hypothetical condition, -
1:44 - 1:48whether an alien is lying or not
won't actually matter. -
1:48 - 1:50To see how that could work,
-
1:50 - 1:54imagine our question
is whether two plus two is four. -
1:54 - 1:55Instead of posing it directly,
-
1:55 - 1:59we say, "If I asked you whether
two plus two is four, -
1:59 - 2:02would you answer 'ozo'?"
-
2:02 - 2:05If 'ozo' means yes
and the overlord is Tee, -
2:05 - 2:07it truthfully replies, "ozo."
-
2:07 - 2:09But what if we ask Eff?
-
2:09 - 2:13Well, it would answer "ulu,"
or no to the embedded question, -
2:13 - 2:17so it lies and replies 'ozo' instead.
-
2:17 - 2:20And if 'ozo' actually means no,
-
2:20 - 2:24then the answer to
our embedded question is 'ulu,' -
2:24 - 2:27and both Tee and Eff still reply 'ozo,'
-
2:27 - 2:29each for their own reasons.
-
2:29 - 2:31If you're confused about why this works,
-
2:31 - 2:34the reason involves logical structure.
-
2:34 - 2:39A double positive and a double negative
both result in a positive. -
2:39 - 2:43Now, we can be sure that asking
either Tee or Eff a question put this way -
2:43 - 2:47will yield 'ozo'
if the hypothetical question is true -
2:47 - 2:50and 'ulu' if it's false
-
2:50 - 2:53regardless of what
each word actually means. -
2:53 - 2:57Unfortunately,
this doesn't help us with Arr. -
2:57 - 3:01But don't worry, we can use our first
question to identify one alien lord -
3:01 - 3:04that definitely isn't Arr.
-
3:04 - 3:08Then we can use the second to find out
whether its Tee or Eff. -
3:08 - 3:09And once we know that,
-
3:09 - 3:13we can ask it to identify
one of the others. -
3:13 - 3:15So let's begin.
-
3:15 - 3:16Ask the alien in the middle,
-
3:16 - 3:22"If I asked you whether the overlord on
my left is Arr, would you answer 'ozo'?" -
3:22 - 3:26If the reply is 'ozo,'
there are two possibilities. -
3:26 - 3:31You could already be talking to Arr,
in which case the answer is meaningless. -
3:31 - 3:35But otherwise, you're talking to either
Tee or Eff, -
3:35 - 3:36and as we know,
-
3:36 - 3:41getting 'ozo' from either one means
your hypothetical question was correct, -
3:41 - 3:45and the left overlord is indeed Arr.
-
3:45 - 3:49Either way, you can be sure the alien
on the right is not Arr. -
3:49 - 3:52Similarly, if the answer is 'ulu,'
-
3:52 - 3:56then you know the alien
on the left can't be Arr. -
3:56 - 4:00Now go to the overlord you've determined
isn't Arr and ask, -
4:00 - 4:04"If I asked 'are you Eff?'
would you answer 'ozo'?" -
4:04 - 4:07Since you don't have to worry about
the random possibility, -
4:07 - 4:11either answer will
establish its identity. -
4:11 - 4:14Now that you know whether its
answers are true or false, -
4:14 - 4:19ask the same alien whether the center
overlord is Arr. -
4:19 - 4:24The process of elimination will identify
the remaining one. -
4:24 - 4:27The satisfied overlords help you
repair your ship -
4:27 - 4:29and you prepare for takeoff.
-
4:29 - 4:33Allowed one final question, you ask
Tee if it's a long way to Earth, -
4:33 - 4:36and he answers "ozo."
-
4:36 - 4:39Too bad you still don't know
what that means.
- Title:
- Can you solve the three gods riddle? - Alex Gendler
- Speaker:
- Alex Gendler
- Description:
-
View full lesson: http://ed.ted.com/lessons/can-you-solve-the-three-gods-riddle-alex-gendler
You and your team have crash-landed on an ancient planet. Can you appease the three alien overlords who rule it and get your team safely home? Created by logician Raymond Smullyan, and popularized by his colleague George Boolos, this riddle has been called the hardest logic puzzle ever. Alex Gendler shows how to solve it.
Lesson by Alex Gendler, animation by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:54
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Jennifer Cody edited English subtitles for Can you solve the three gods riddle? |