Return to Video

Can you solve the riddle and escape Hades? - Dan Finkel

  • Not Synced
    Maybe the fates got clumsy.
  • Not Synced
    Maybe Poseidon had one of his angry days.
  • Not Synced
    However it happened, the
    underworld is overcrowded,
  • Not Synced
    and Zeus has ordered Hades
    to let some spirits out.
  • Not Synced
    Hades arranges all the souls of the
    dead in a line before Cerberus.
  • Not Synced
    When one of his three heads bites
    down on the soul in front of it,
  • Not Synced
    they’ll get returned to the
    land of the living.
  • Not Synced
    Anyone to the left must get out of
    line and stay in Hades forever.
  • Not Synced
    And everyone else shuffles forward,
    at which point Cerberus will feed again.
  • Not Synced
    Each of the dog’s heads has an equal
    chance of being the one to bite each time,
  • Not Synced
    and no two ever bite simultaneously.
  • Not Synced
    Unfortunately, Hades’ minions forgot
    to tell you what was happening,
  • Not Synced
    and by the time you show up there are
    only 99 souls left in line.
  • Not Synced
    Hades looks furious and drawing attention
    to yourself won’t end well.
  • Not Synced
    But suddenly, time freezes, and Hermes
    steps out of the shadows.
  • Not Synced
    He tells you he can instantly put you into
    the line,
  • Not Synced
    and no one will realize what happened.
  • Not Synced
    But he’ll only grant his grace to someone
    clever enough
  • Not Synced
    to take full advantage of it.
  • Not Synced
    Choose the best place in line and
    he’ll give you the spot.
  • Not Synced
    Choose wrong, and he’ll leave you to rot.
  • Not Synced
    Which spot should you pick?
  • Not Synced
    It’s possible to calculate the exact
    probability of going free
  • Not Synced
    in all 100 spots.
  • Not Synced
    But there’s a much simpler path to
    the solution
  • Not Synced
    that requires surprisingly
    little calculation.
  • Not Synced
    Imagine being anywhere in line.
  • Not Synced
    Way up at the front, one of the three
    heads will pick someone at random,
  • Not Synced
    and you’ll move forward 1, 2, or 3 spaces.
  • Not Synced
    Since each is equally likely,
  • Not Synced
    your chance of survival from wherever
    you started
  • Not Synced
    is the average of the chances from
    each of the three spaces in front of you.
  • Not Synced
    And this is where you can
    find a huge shortcut.
  • Not Synced
    Averages must be on or between the
    extremes of what you’re averaging––
  • Not Synced
    they can never be higher than the
    highest value or lower than the lowest.
  • Not Synced
    So whatever your chances of survival
    are where you start,
  • Not Synced
    one of the three places in front
    of you is at least as good,
  • Not Synced
    and probably better.
  • Not Synced
    This observation is incredibly powerful.
  • Not Synced
    It means that wherever you are in line,
  • Not Synced
    it’d be wise to trade your place for one
    of the three spots in front of you.
  • Not Synced
    Let’s ignore which for now and think of
    them as a trio––
  • Not Synced
    this trio’s maximum value is better than
    this trio’s, and so on.
  • Not Synced
    Keep going and you’ll reach the front...
  • Not Synced
    These three spots must contain the
    extreme values––
  • Not Synced
    the best and worst probabilities––
  • Not Synced
    for the entire line. In other words,
  • Not Synced
    they’re all we need to consider.
  • Not Synced
    Place 1 is bad.
  • Not Synced
    Head one would save you, and the other
    two doom you forever.
  • Not Synced
    That’s just a 1 in 3 chance to escape.
  • Not Synced
    Place 2 is better: head two is great,
  • Not Synced
    head 3 is bad, and head 1 is ok
    in that it gives you another chance.
  • Not Synced
    But place 3 is best, because head
    3 saves you
  • Not Synced
    while heads 1 and 2 both
    give you extra chances.
  • Not Synced
    If you did want to consider the exact
    probabilities,
  • Not Synced
    the odds of surviving in place 3 are 16
    out of 27, or close to 60%.
  • Not Synced
    The spots later in line tend to be very
    close to having a 50% chance of survival.
  • Not Synced
    Why 50%?
  • Not Synced
    Because every time Cerberus sends
    one soul up to be reborn,
  • Not Synced
    he leaves 0, 1, or 2 souls
    in the underworld.
  • Not Synced
    That averages out to one person
    staying for each one who gets freed.
  • Not Synced
    But you can beat those odds handily
    with what you now know.
  • Not Synced
    Hermes has places to be, and so do you.
  • Not Synced
    He rewards your insight by sneaking
    you into the third spot.
  • Not Synced
    And 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:

more » « less
Video Language:
English
Team:
TED
Project:
TED-Ed
Duration:
04:24

English subtitles

Revisions Compare revisions