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

譯者: C Cheng 審譯者: Helen Chang

Maybe the fates got clumsy.

Maybe Poseidon had one of his angry days.

也許波賽頓經歷了憤怒的一日。

However it happened, the underworld is overcrowded,

不論是如何發生的， 冥界變得十分擁擠。

and Zeus has ordered Hades to let some spirits out.

於是，宙斯命令冥王 哈迪斯釋放一些靈魂。

Hades arranges all the souls of the dead in a line before Cerberus.

哈迪斯讓所有死去的靈魂在 地獄犬面前排成一隊。

When one of his three heads bites down on the soul in front of it,

當牠三個頭中的一個 咬住牠面前的靈魂時，

they’ll get returned to the land of the living.

這些靈魂就會重返人間。

Anyone to the left must get out of line and stay in Hades forever.

在其左側的必須離開隊伍， 永遠留在冥界。

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

所有其他人則向前推進， 此時地獄犬將再次進食。

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

每次，每個頭都有同等的咬食機會，

and no two ever bite simultaneously.

而且遠永不會有兩個頭同時咬食。

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

不幸的是，哈迪斯的僕從 忘記告訴你正在發生的這件事，

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

等你露面時，只剩下 99 個靈魂在排隊。

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

哈迪斯看上去很生氣， 而且引起他注意自己不會有好下場。

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

突然時間停止了。

赫耳墨斯從陰影裡走了出來。

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

他對你說，他可以 把你立即放入隊伍中，

and no one will realize what happened.

而且不會有人意識到發生了什麼。

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

但是，他只將恩典賜予足夠聰明，

to take full advantage of it.

可以充分利用它的人。

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

如果選擇了隊伍中的最佳位置， 他就會把那個位置給你。

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

如果選錯了，他則會讓你自生自滅。

Which spot should you pick?

你會選擇哪個位置？

Pause the video to figure it out yourself.

【暫停視頻，自行解題】 【答案揭曉，3 秒】

Answer in 3

Answer in 2

【答案揭曉，2 秒】

Answer in 1

【答案揭曉，1 秒】

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

對這 100 個位置的獲釋概率 一一加以計算是有可能的。

in all 100 spots.

But there’s a much simpler path to the solution

但是，有一條更為簡單的解決途徑，

that requires surprisingly little calculation.

它幾乎不需要什麼計算。

Imagine being anywhere in line.

想像站在隊伍裡的任何一個地方。

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

在隊伍的前方，三個頭中的 一個將隨機挑選一個人，

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

之後你要向前移動 1，2，或者 3 個位置。

Since each is equally likely,

由於可能性均等，

your chance of survival from wherever you started

因此無論從哪裡開始，你的倖存機會

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

都會是你前面三個位置的平均機會。

And this is where you can find a huge shortcut.

就在這裡你可以發現一個大捷徑。

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

平均數必須是均值， 或者處在被平均的極值之內——

they can never be higher than the highest value

絕不可能高於最高值

or lower than the lowest.

或低於最低值。

So whatever your chances of survival are where you start,

因此，無論你起始 位置的倖存機率如何，

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

你前面三個位置中的一個 至少與你的位置一樣好，

and probably better.

甚至可能更好。

This observation is incredibly powerful.

這一觀察非常有力。

It means that wherever you are in line,

這就意味著無論你在 隊伍中的哪個位置上，

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

明智之舉是將你的位置換成 前面三個位置中的一個。

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

讓我們暫且忽略具體是哪一個， 而將它們視為一個三件組合——

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

這個組合的最大值 好過這個組合，依此類推。

Keep going and you’ll reach the front...

繼續下去，你將到達隊伍的最前面。

These three spots must contain the extreme values—

這三個位置中必定包含了極值——

the best and worst probabilities—

即在整個隊伍中的最佳和最差機率，

for the entire line.

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

換句話說，是我們需要考慮的全部。

Place 1 is bad.

第 1 個位置很糟。

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

第 1 個頭會放過你， 而另兩個將使你萬劫不復，

That’s just a 1 in 3 chance to escape.

也就是逃生機會只有三分之一。

Place 2 is better: head two is great,

第 2 個位置好一些。

第 2 個頭不錯，

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

第 3 個頭很糟，

而第 1 個頭還可以，給你另一次機會。

But place 3 is best, because head 3 saves you

但是第 3 個位置最好。

因為第 3 個頭放過你，

while heads 1 and 2 both give you extra chances.

同時第 1 個和第 2 個頭 給你多出來的機會。

If you did want to consider the exact probabilities,

如果你確實想知道準確概率的話，

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

那麼第 3 個位置的倖存機率是 27 分之 16，或接近於 60％。

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

隊伍後面的位置基本具有 將近 50％ 的倖存機會。

Why 50%?

為什麼是 50％？

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

因為每當地獄犬送一個靈魂去重生，

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

就會在冥界中留下 0、1 或 2 個靈魂。

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

平均每釋放一個人就會 有另一個人被留下。

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

但是利用你現在所知道的， 你可以輕鬆克服這些難關。

Hermes has places to be, and so do you.

赫耳墨斯還有事要做，你也一樣。

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

他將獎勵你的洞見， 把你偷偷插入到第三個位置上。

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

從那裡起，無需久等， 你便會知道最終的命運。