is to bring sunlight into a vampire's lair.

就是把陽光帶進吸血鬼的巢穴裡。

You've stealthily descended into the darkness of a vampire cave,

你已經偷偷地潛入 吸血鬼的黑暗洞口，

setting a sequence of mirrors as you go.

把一面一面的鏡子按角度架起來。

When the sun reaches the right angle in the sky,

當外面的太陽冉冉升起的時候，

a focused beam of light will ricochet along the mirrors,

一束陽光會被鏡子折射到洞內，

strike your diffuser,

打到你準備好的聚光燈上，

and illuminate the great chamber where the vampires sleep.

然後就可以照亮吸血鬼們睡覺的大堂。

You set the final mirror

你把最後一面鏡子架好，

and sneak through an opening in the corner of the great chamber.

然後偷偷潛入了大堂的一角。

The diffuser must be wall-mounted,

聚光燈只能被安在牆上，

but the walls are crowded with coffins,

但幾乎​​所有的牆附近 都有吸血鬼睡覺的棺材，

which you don't dare disturb.

所以你不敢去把他們吵醒。

The only open spots are in the other three corners of the room.

只有大堂內的其它三個角落有空隙。

The light will enter through the southwest corner at a 45 degree angle

這束陽光會從西南角 以 45 度方向進入，

and bounce off the perfectly smooth metallic walls

然後會在大堂內光滑的四壁折射，

until it hits one of the other three corners.

直到這束光打到 另外三個角中的其中一角。

But which corner will it hit?

但是，到底哪一個角落會被擊中呢？

You know the room is a rectangle 49 meters wide and 78 meters long.

你知道這個大堂是一個 49 公尺寬 78 公尺長的長方形，

You could probably find the answer

你估計可以這樣慢慢找到答案：

by drawing a scale model of the room and tracing the path of the light,

把大堂按比例畫在紙上， 然後追尋光的軌跡，

but the sun will be in its place in just minutes,

但是太陽馬上就要升起了，

and you've got no time to spare.

你沒法浪費時間。

Fortunately, there's a different way to solve this puzzle

不過好在還有另一種方法 可以解決這個難題，

that's both simple and elegant.

既簡單又優雅。

So in which corner should you place the diffuser

那現在讓我們看看， 到底在哪個角落放聚光燈，

to flood the vampire lair with sunlight?

才能成功殺死吸血鬼呢？

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

如果你想自己思考答案， 可以現在暫停影片。

Answer in 2

離答案公佈還有：2 秒

Answer in 1

1 秒

You could tackle this problem by examining smaller rooms,

想要解決這道題， 可以先看看小一點的房間，

and you'd find a lot of interesting patterns.

然後你會發現一些有意思的規律。

But there's one insight that can unravel this riddle in almost no time at all.

有一個秘訣可以讓你 迅速解決這道難題。

Let's draw the chamber on a coordinate grid,

讓我們先把這個大堂 按比例畫在圖紙上，

with the Southwest corner at the point (0,0).

把西南角的座標定為（0，0）。

The light passes through grid points

這束陽光的軌跡 射入的座標點有一個共同性：

with coordinates that are either both even or both odd.

兩座標要麼都是偶數， 要麼都是奇數。

This is true even after it bounces off one or more walls.

即使光束經過多次的 牆壁反彈後仍是如此。

Another way of thinking about it is this:

換種方法解釋，就是說：

since the light travels at a 45 degree angle,

因為這束光 是以 45 度角折射進入的，

it always crosses the diagonal of a unit square.

所以它只會沿著 每一個方格的對角線走，

Traveling 1 meter horizontally changes the x coordinate

橫著移動 1 公尺 等於在 x 軸上移一格，

from even to odd or vice versa.

把偶數變成奇數，或者相反。

Traveling 1 meter vertically changes the y coordinate

豎著移動 1 公尺 等於在 y 軸上移一格，

from even to odd or vice versa.

把偶數變成奇數，或者相反。

Traveling diagonally – as the light does here – does both at once,

沿著對角線走就是橫豎都移動，

so the x and y coordinates of any points the light passes through

所以，這束光經過的任何一點，

must be both even, or both odd.

一定是兩座標都是偶數， 或者兩座標都是奇數。

This observation is more powerful than it seems.

這觀察就是解決這道題的關鍵。

In particular, it means that we have a way to identify the kinds of points

也就是說，我們找到了 一個規律來辨識

the light won't ever go through

光不會經過的點。

If one of the coordinates is even and the other is odd,

如果某個點的一個座標是偶數， 另一座標是奇數，

the light will miss them.

那麼光就不會經過。

That means it'll miss the top two corners of the room,

也就是，這束光不會打到 大堂的上面兩個角，

since those points have one even and one odd coordinate.

因為這兩個角的縱橫座標 是一奇、一偶。

The Southeast corner is the only option for the diffuser.

也就是說，東南角 是唯一可以放聚光燈的地方。

And indeed, when that precious beam of sunlight enters the hall,

果然，當那束寶貴的陽光 打進大堂的時候，

it bounces between the walls

它沿著四壁折射，

and strikes the Southeast corner, spot on.

最後集中了東南角的聚光燈！

The vampires, sensing the intrusion,

這時，吸血鬼們發現了有入侵者，

burst from their coffins and turn to dust in the light.

他們從棺材裡爬出來， 但是被陽光化為灰燼。

It was a “high stakes” test,

這是一道「高風險」的問題，

and you passed with flying colors.

你大獲全勝！