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譯者: Lilian Chiu
審譯者: Helen Chang
00:06
You heard the traveler's tales,
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你聽了旅人的故事,
00:08
you followed the crumbling maps,
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你遵循著破爛的地圖,
00:10
and now, after a long and dangerous quest,
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經過了驚險漫長的探索之旅後,
00:12
you have some good news and some bad news.
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你有些好消息也有些壞消息。
00:16
The good news is you've managed to locate
the legendary dungeon
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好消息是,你得以
找到了傳說地牢的位置,
00:19
containing the stash
of ancient Stygian coins
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地牢裡藏著古老的冥河硬幣,
00:22
and the eccentric wizard
who owns the castle
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而擁有這座城堡的古怪巫師
00:25
has even generously
agreed to let you have them.
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甚至已經慷慨地同意讓你拿走它們。
00:29
The bad news is that he's not
quite as generous
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壞消息是他沒那麼慷慨,
00:31
about letting you leave the dungeon,
unless you solve his puzzle.
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你若解不開他的謎題,
就不能離開地牢。
00:37
The task sounds simple enough.
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這項任務聽起來挺簡單。
00:39
Both faces of each coin bear
the fearsome scorpion crest,
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每個硬幣的兩面都有
駭人的蠍子紋飾,
00:44
one in silver,
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一面是銀色,
00:45
one in gold.
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一面是金色。
00:47
And all you have to do is separate them
into two piles
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你所要做的就是將硬幣分成兩堆,
00:50
so that each has the same number
of coins facing silver side up.
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每堆中銀色面朝上的
硬幣數量都相同。
00:56
You're about to begin when all
of the torches suddenly blow out
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你正要開始時,
突然所有的火炬都熄滅了,
01:00
and you're left in total darkness.
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你身處在一片漆黑當中。
01:02
There are hundreds
of coins in front of you
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你面前有數百個硬幣,
01:05
and each one feels the same on both sides.
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且每個硬幣的兩面摸起來都一樣。
01:08
You try to remember
where the silver-facing coins were,
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你試著回憶銀色面的硬幣在哪裡,
01:11
but it's hopeless.
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但毫無希望。
01:13
You've lost track.
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你已經想不起來了。
01:14
But you do know one thing for certain.
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但有一件事是你能確定的。
01:17
When there was still light,
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當還有光時,
01:18
you counted exactly
20 silver-side-up coins in the pile.
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你算出在這一堆硬幣中剛好
有 20 個是銀色面朝上。
01:23
What can you do?
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你能怎麼做?
01:24
Are you doomed to remain in the dungeon
with your newfound treasure forever?
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你注定要和你新發現的寶藏
永遠困在地牢中嗎?
01:29
You're tempted to kick the pile of coins
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你很想踹那堆硬幣一腳,
01:31
and curse the curiosity
that brought you here.
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並咒罵引導你來這裡的好奇心。
01:34
But at the last moment, you stop yourself.
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但在最後一刻,你阻止了自己。
01:37
You just realized there's
a surprisingly easy solution.
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你意識到有一個非常簡單的解答。
01:41
What is it?
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解答是什麼?
01:43
Pause here if you want to figure
it out for yourself.
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如果你想自己解出,請在此暫停。
01:46
Answer in: 3
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解答倒數:3。
01:47
Answer in: 2
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解答倒數:2。
01:49
Answer in: 1
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解答倒數:1。
01:50
You carefully move aside 20 coins
one by one.
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你小心地將 20 個硬幣
一一移到旁邊。
01:54
It doesn't matter which ones:
any coins will do,
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選哪個硬幣都無所謂:
任何硬幣都可以。
01:57
and then flip each one of them over.
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然後將它們每一個都翻面。
02:00
That's all there is to it.
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要做的就只有這樣。
02:02
Why does such a simple solution work?
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為何如此簡單的解答行得通呢?
02:04
Well, it doesn't matter how many
coins there are to start with.
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一開始有多少個硬幣並不重要。
02:08
What matters is that only 20
of the total are facing silver side up.
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重要的是全部的硬幣中
只有 20 個是銀色面朝上的。
02:12
When you take 20 coins in the darkness,
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當你在黑暗中拿取 20 個硬幣,
02:15
you have no way of knowing how many
of these silver-facing coins
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你不可能知道在新選出來的這一堆
02:19
have ended up in your new pile.
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硬幣中有多少是銀面朝上的。
02:21
But let's suppose you got 7 of them.
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假設你拿到了 7 個銀面朝上的。
02:24
This means that there are 13
silver-facing coins left
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那就表示還有 13 個
銀面朝上的硬幣
02:27
in the original pile.
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留在原本的那堆硬幣中。
02:29
It also means that the other
13 coins in your new pile
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那也意味著在新的那堆硬幣裡,
02:33
are facing gold side up.
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有 13 個金面朝上的硬幣。
02:35
So what happens when you flip
all of the coins in the new pile over?
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所以當你把新的那堆硬幣
全部翻面,會發生什麼事?
02:40
Seven gold-facing coins and
13 silver-facing coins
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會有 7 個金面朝上的銀幣,
和 13 個銀面朝上的硬幣,
02:44
to match the ones in the original pile.
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銀面朝上的硬幣數就和
原本那堆硬幣相符了。
02:47
It turns out this works no matter how
many of the silver-facing coins you grab,
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最後發現,結果都是相同的,
不論你拿到幾個銀面朝上的硬幣,
02:52
whether it's all of them,
a few, or none at all.
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不論是全部、幾個,
還是一個也沒有。
02:56
That's because of what's known
as complementary events.
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原因是所謂的互補事件。
03:00
We know that each coin only has
two possible options.
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我們已經知道每個硬幣
只有兩個可能性。
03:04
If it's not facing silver side up,
it must be gold side up,
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若不是銀面朝上,
就是一定是金面朝上。
03:08
and vice versa,
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反之亦然,
03:09
and in any combination of 20 coins,
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不論這 20 個硬幣是怎樣的組合,
03:12
the number of gold-facing
and silver-facing coins
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銀面朝上的硬幣數
和金面朝上的硬幣數
03:15
must add up to 20.
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加起來一定是 20。
03:17
We can prove this mathematically
using algebra.
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我們可以用代數
來做數學上的證明。
03:20
The number of silver-facing coins
remaining in the original pile
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留在原本那一堆硬幣中的
銀面朝上硬幣數目
03:24
will always be 20 minus
however many you moved to the new pile.
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一定會等於 20 減去被拿到
新的那堆的銀面朝上硬幣數目。
03:29
And since your new pile also
has a total of 20 coins,
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既然新的那堆硬幣中的
硬幣總數也是 20,
03:32
its number of gold-facing coins will be
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在這堆硬幣中金面朝上的
硬幣數目就會是
03:35
20 minus the amount of
silver-facing coins you moved.
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20 減去被你移動的
銀面朝上硬幣數目。
03:39
When all the coins in the new pile
are flipped,
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當新的這堆硬幣中
所有硬幣都翻了一面,
03:42
these gold-facing coins become
silver-facing coins,
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金面朝上的硬幣
就變成了銀面朝上,
03:45
so now the number of silver-facing
coins in both piles is the same.
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現在,兩堆硬幣中銀面朝上的
硬幣數目就相同了。
03:51
The gate swings open
and you hurry away with your treasure
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大門被打開了,
你在女巫改變心意之前
03:55
before the wizard changes his mind.
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拿著寶藏立刻離開。
03:57
At the next crossroads, you flip
one of your hard-earned coins
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在下個十字路口,你投擲了
其中一個得來不易的硬幣,
04:00
to determine the way
to your next adventure.
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來決定你下次探險的方向。
04:03
But before you go, we have another
quick coin riddle for you –
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但是在你離開前,我們還為你
準備了另一個硬幣謎題——
04:07
one that comes from this video
sponsor’s excellent website.
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這個謎題來自這支影片
贊助商的傑出網站。
04:11
Here we have 8 arrangements of coins.
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這裡我們有 8 種不同的硬幣排列。
04:14
You can flip over adjacent pairs of coins
as many times as you like.
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你可以翻轉相鄰的一對硬幣,
翻轉次數不限。
04:18
A flip always changes gold to silver,
and silver to gold.
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翻轉就會把金色轉為銀色,
銀色轉為金色。
04:22
Can you figure out how to tell,
at a glance,
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你能不能想出,要如何只看一眼,
04:26
which arrangements can be made all gold?
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就知道哪種排列最後
可以轉為全部金色?
04:29
You can try an interactive version of
this puzzle and confirm your solution
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你可以在 Brilliant 的網站上
玩這個遊戲的互動版,
04:33
on Brilliant’s website.
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來確認你的答案對不對。
04:36
We love Brilliant.org because the site
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04:39
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04:42
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or limited cases,
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04:47
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04:49
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04:52
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04:55
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04:59
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05:02
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05:05
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05:09
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05:12
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