that's been terrorizing your town.

他一直在威脅你的小鎮。

After months of detective work,

經過數個月的偵察，

you've narrowed your suspects to one of five people:

你已經把嫌疑犯減少到五個人：

the mayor,

市長、裁縫師、麵包師傅、

the tailor,

雜貨商，或是木匠。

the baker,

你邀請他們吃晚餐， 心中有個簡單的計畫：

the grocer,

你要在每個人的晚餐中都偷偷

or the carpenter.

放入一片很稀有的 正方形狼人解藥。

You've invited them to dinner with a simple plan:

不幸的是，你的寵物山羊

you'll slip a square of a rare werewolf antidote

吃掉了四片解藥，只剩下一片。

into each of their dinners.

幸運的是，剩下的 那一片解藥有五十克，

Unfortunately, your pet goat just ate four of the squares,

最低有效劑量是十克。

and you only have one left.

如果你能精確地 把這片解藥分為五份，

Luckily, the remaining square is 50 grams,

你就能給每一個人足夠的解藥。

and the minimum effective dose is 10 grams.

你會需要用雷射 切割工具來切藥片；

If you can precisely divide the square into fifths

你能用的其他方式都不夠精確。

you'll have just enough antidote for everyone.

有八個點可以當作每次切割的

You'll have to use a laser-cutting tool to cut up the square;

起始點或是終點。

every other means available to you isn't precise enough.

若要使用這個裝置， 你需要輸入兩個點，

There are 8 points that can act as starting or ending points for each cut.

告訴雷射每次切割 從哪裡開始、哪裡結束，

To use the device, you'll have to input pairs of points

接著雷射會同時執行所有的切割。

that tell the laser where to begin and end each cut,

你想要把藥片切成幾塊都可以，

and then the laser executes all the cuts simultaneously.

只要你能把它們湊成 十克的份量即可。

It's okay to cut the square into as many pieces as you want,

但你不能將藥片對折 或是用其他方式改變它，

as long as you can group them into 10 gram portions.

你使用雷射切割器的 機會只有一次。

But you can't fold the square or alter it otherwise,

馬上就要滿月了，屆時就會有人

and you only get one shot at using the laser cutter.

變身狼人把你撕成碎片，

The full moon is rising,

除非你在這之前就把他們治癒。

and in a moment someone will transform and tear you all apart

你要如何把解藥完美平分成五份，

unless you can cure them first.

治癒秘密狼人，拯救大家？

How can you divide the antidote into perfect fifths,

如果你想要嘗試自己 解題，在這裡暫停。

cure the secret werewolf, and save everyone?

答案即將公佈：三

Pause the video now if you want to figure it out for yourself.

答案即將公佈：二

Answer in 3

答案即將公佈：一

Answer in 2

對於切割和重新排列的謎題，

Answer in 1

通常很有用的做法就是 真的拿一張紙出來，

When it comes to puzzles that involve cutting and rearranging,

把它切割開，試試看 你能得到什麼結果。

it's often helpful to actually take a piece of paper

如果我們切割 BF 和 DH，

and try cutting it up to see what you can get.

就會得到四份，但我們需要五份。

If we cut BF and DH we'd get fourths, but we need fifths.

也許有方法可以把四分之一再去掉 一點點，得到精確的五分之一。

Maybe there's a way to shave a bit off of a quarter to get exactly one fifth.

一開始，切割 BE 看起來不錯，

Cutting BE looks good at first, but that last cut

但最後一次切割會拿掉 四分之一的四分之一，

takes a off a quarter of a quarter,

讓我們得到十六分之三，

leaving us with a portion of 3/16: just smaller than a fifth,

比五分之一少一點，

and not enough to cure a werewolf.

這劑量不夠治癒一個狼人。

What if we started with BE instead?

如果我們改從 BE 開始呢？

That would also give us a quarter.

那也會讓我們得到四分之一。

And is there a way to shave just a bit more off?

有什麼方法可以 再多切掉一小部分嗎？

Both DG and CH look promising.

DG 和 CH 看起來都很理想。

If we make one more cut, from A to F,

如果我們再多切割 一次，從 A 到 F，

we may start to notice something.

我們會開始注意到一些狀況。

With these four cuts—from B to E, D to G, F to A,

若切割這四條線——

and H to C—we've got four triangles

B 到 E、D 到 G、F 到 A、H 到 C ——

and a square in the middle.

我們會得到四個三角形， 中間有一個正方形。

But the pieces that make each triangle can also be

但組成每一個三角形的切片都能夠

rearranged to make a square identical to the middle one.

被重新排列成一個正方形， 跟中間的一模一樣。

This means that we've split the antidote into perfect fifths!

那就表示，我們把解藥 完美地分成五份了！

What's interesting about this sort of problem

關於這類問題，很有趣的就是

is that while it's possible to solve it by starting from the geometry,

雖然的確可能可以從幾何學開始，

it's actually easier to start experimenting and see where that gets you.

但用試驗的方式其實更容易些。

That wouldn't be as viable if the square had, say, 24 cut points,

如果方形藥片有比如二十四個點， 這招就不見得那麼可行了，

but with just 8 there are only so many reasonable options.

但只有八個點時， 合理的選項就只有那麼多。

You secretly dose each of the townspeople

當滿月出現時，你偷偷地

as the full moon emerges in the sky.

在每個鎮民的食物中下藥。

And just as you do, a terrible transformation begins.

你正在下藥時， 可怕的變身開始了。

Then, just as suddenly, it reverses.

接著，突然，變身反轉了。

Your measurements were perfect,

你測量的劑量恰到好處，

and the people and animals of the town can rest a little easier.

這個小鎮的居民和動物 能夠更輕鬆地休息了。