Can you solve the riddle and escape Hades? - Dan Finkel
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0:08 - 0:09Maybe the fates got clumsy.
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0:09 - 0:12Maybe Poseidon had one of his angry days.
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0:12 - 0:16However it happened,
the underworld is overcrowded, -
0:16 - 0:20and Zeus has ordered Hades
to let some spirits out. -
0:20 - 0:25Hades arranges all the souls
of the dead in a line before Cerberus. -
0:25 - 0:28When one of his three heads bites
down on the soul in front of it, -
0:28 - 0:31they’ll get returned
to the land of the living. -
0:31 - 0:36Anyone to the left must get out
of line and stay in Hades forever. -
0:36 - 0:42And everyone else shuffles forward,
at which point Cerberus will feed again. -
0:42 - 0:47Each of the dog’s heads has an equal
chance of being the one to bite each time, -
0:47 - 0:51and no two ever bite simultaneously.
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0:51 - 0:55Unfortunately, Hades’ minions forgot
to tell you what was happening, -
0:55 - 1:00and by the time you show up
there are only 99 souls left in line. -
1:00 - 1:05Hades looks furious and drawing attention
to yourself won’t end well. -
1:05 - 1:10But suddenly, time freezes,
and Hermes steps out of the shadows. -
1:10 - 1:13He tells you he can instantly put
you into the line, -
1:13 - 1:16and no one will realize what happened.
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1:16 - 1:20But he’ll only grant his grace
to someone clever enough -
1:20 - 1:21to take full advantage of it.
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1:21 - 1:24Choose the best place in line
and he’ll give you the spot. -
1:24 - 1:28Choose wrong, and he’ll leave you to rot.
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1:28 - 1:30Which spot should you pick?
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1:30 - 1:32Pause the video to figure it out yourself.
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1:32 - 1:33Answer in 3
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1:33 - 1:35Answer in 2
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1:35 - 1:38Answer in 1
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1:38 - 1:42It’s possible to calculate the exact
probability of going free -
1:42 - 1:44in all 100 spots.
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1:44 - 1:47But there’s a much simpler path
to the solution -
1:47 - 1:50that requires surprisingly
little calculation. -
1:50 - 1:52Imagine being anywhere in line.
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1:52 - 1:56Way up at the front, one of the three
heads will pick someone at random, -
1:56 - 2:00and you’ll move forward 1, 2, or 3 spaces.
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2:00 - 2:02Since each is equally likely,
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2:02 - 2:05your chance of survival
from wherever you started -
2:05 - 2:11is the average of the chances from
each of the three spaces in front of you. -
2:11 - 2:15And this is where you can
find a huge shortcut. -
2:15 - 2:21Averages must be on or between
the extremes of what you’re averaging— -
2:21 - 2:24they can never be higher
than the highest value -
2:24 - 2:26or lower than the lowest.
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2:26 - 2:29So whatever your chances of survival
are where you start, -
2:29 - 2:34one of the three places in front
of you is at least as good, -
2:34 - 2:35and probably better.
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2:35 - 2:39This observation is incredibly powerful.
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2:39 - 2:41It means that wherever you are in line,
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2:41 - 2:46it’d be wise to trade your place for one
of the three spots in front of you. -
2:46 - 2:50Let’s ignore which for now and think
of them as a trio— -
2:50 - 2:55this trio’s maximum value
is better than this trio’s, and so on. -
2:55 - 2:57Keep going and you’ll reach the front...
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2:57 - 3:02These three spots must contain
the extreme values— -
3:02 - 3:04the best and worst probabilities—
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3:04 - 3:06for the entire line.
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3:06 - 3:10In other words,
they’re all we need to consider. -
3:10 - 3:11Place 1 is bad.
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3:11 - 3:15Head one would save you, and the other
two doom you forever. -
3:15 - 3:18That’s just a 1 in 3 chance to escape.
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3:18 - 3:21Place 2 is better: head two is great,
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3:21 - 3:27head 3 is bad, and head 1 is ok
in that it gives you another chance. -
3:27 - 3:31But place 3 is best,
because head 3 saves you -
3:31 - 3:36while heads 1 and 2 both
give you extra chances. -
3:36 - 3:39If you did want to consider
the exact probabilities, -
3:39 - 3:46the odds of surviving in place 3
are 16 out of 27, or close to 60%. -
3:46 - 3:52The spots later in line tend to be very
close to having a 50% chance of survival. -
3:52 - 3:53Why 50%?
-
3:53 - 3:57Because every time Cerberus sends
one soul up to be reborn, -
3:57 - 4:02he leaves 0, 1, or 2 souls
in the underworld. -
4:02 - 4:07That averages out to one person
staying for each one who gets freed. -
4:07 - 4:11But you can beat those odds handily
with what you now know. -
4:11 - 4:14Hermes has places to be, and so do you.
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4:14 - 4:18He rewards your insight by sneaking
you into the third spot. -
4:18 - 4:22And from there it’ll be just a short wait
to learn your ultimate fate.
- Title:
- Can you solve the riddle and escape Hades? - Dan Finkel
- Speaker:
- Dan Finkel
- Description:
-
View full lesson: https://ed.ted.com/lessons/can-you-solve-the-riddle-and-escape-hades-dan-finkel
The underworld is overcrowded, and Zeus has ordered Hades to let some spirits out. Hades arranges all the souls of the dead in a line before Cerberus. When one of his three heads bites down on the soul in front of it, they'll get returned to the land of the living. Anyone to the left must stay in Hades forever. Can you pick the right spot and escape the underworld? Dan Finkel shows how.
Lesson by Dan Finkel, directed by Artrake Studio.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 04:24
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Tara Ahmadinejad edited English subtitles for Can you solve the riddle and escape Hades? |