Name: Can you solve the riddle and escape Hades? - Dan Finkel
Uploaded: 2020-10-23T22:20:19.000Z
Duration: 5 min
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Maybe Poseidon had one of his angry days.

Transition words & phrases

However it happened,  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 get out  of line and stay in Hades forever.

And everyone else shuffles forward, at which point Cerberus will feed again.

Each of the dog's heads has an equal chance of being the one to bite each time,

Unfortunately, Hades' minions forgot to tell you what was happening,

and by the time you show up  there are only 99 souls left in line.

Hades looks furious and drawing attention to yourself won't end well.

But suddenly, time freezes,  and Hermes steps out of the shadows.

He tells you he can instantly put  you into the line,

But he'll only grant his grace  to someone clever enough

Choose the best place in line  and he'll give you the spot.

Choose wrong, and he'll leave you to rot.

Pause the video to figure it out yourself.

It's possible to calculate the exact  probability of going free

But there's a much simpler path  to the solution

that requires surprisingly little calculation.

Way up at the front, one of the three heads will pick someone at random,

and you'll move forward 1, 2, or 3 spaces.

your chance of survival  from wherever you started

is the average of the chances from each of the three spaces in front of you.

And this is where you can find a huge shortcut.

Averages must be on or between  the extremes of what you're averaging—

they can never be higher  than the highest value

So whatever your chances of survival are where you start,

one of the three places in front  of you is at least as good,

it'd be wise to trade your place for one of the three spots in front of you.

Let's ignore which for now and think  of them as a trio—

this trio's maximum value  is better than this trio's, and so on.

These three spots must contain  the extreme values—

In other words, they're all we need to consider.

Head one would save you, and the other two doom you forever.

head 3 is bad, and head 1 is ok in that it gives you another chance.

But place 3 is best,  because head 3 saves you

while heads 1 and 2 both give you extra chances.

If you did want to consider  the exact probabilities,

the odds of surviving in place 3  are 16 out of 27, or close to 60%.

The spots later in line tend to be very  close to having a 50% chance of survival.

Because every time Cerberus sends one soul up to be reborn,

he leaves 0, 1, or 2 souls in the underworld.

That averages out to one person staying for each one who gets freed.

But you can beat those odds handily with what you now know.

He rewards your insight by sneaking  you into the third spot.

And from there it'll be just a short wait  to learn your ultimate fate.

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

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