Can you solve the vampire hunter riddle? - Dan Finkel

翻译人员: Jiayao Li 校对人员: Lipeng Chen

The greatest challenge a vampire hunter can take on

一个吸血鬼猎人 能完成的最伟大的任务，

is to bring sunlight into a vampire's lair.

就是把阳光带进吸血鬼的巢穴里。

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

你已经偷偷地潜入了 吸血鬼的黑暗洞口，

setting a sequence of mirrors as you go.

把一面一面的镜子按角度架起来。

When the sun reaches the right angle in the sky,

当外面的太阳升起到 一定角度的时候，

a focused beam of light will ricochet along the mirrors,

一束阳光会被镜子折射到洞内，

strike your diffuser,

打到你准备好的聚光灯上，

and illuminate the great chamber where the vampires sleep.

然后就可以照亮 吸血鬼们睡觉的大堂。

You set the final mirror

你把最后一面镜子架好，

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

然后偷偷潜入了大堂的一角。

The diffuser must be wall-mounted,

聚光灯只能被安在墙上，

but the walls are crowded with coffins,

但几乎所有的墙附近 都有吸血鬼睡觉的棺材，

which you don’t dare disturb.

所以你不敢去把他们吵醒。

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

唯一可行的就是 大堂内的其它三个角落。

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

这束阳光会从西南角 以45度方向进入，

and bounce off the perfectly smooth metallic walls

然后会在大堂内光滑的四壁折射，

until it hits one of the other three corners.

直到这束光打到 另外三个角中的其中一角。

But which corner will it hit?

但是，到底哪一个角落会被击中呢?

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

你知道这个大堂是一个 49米宽78米长的长方形。

You could probably find the answer

你估计可以这样慢慢找到答案：

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

把大堂按比例画在纸上， 然后追寻光的轨迹，

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

但是太阳马上就要升起了，

and you’ve got no time to spare.

你没法浪费时间。

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

不过好在，还有另一种方法 可以解决这个难题，

that’s both simple and elegant.

这种方法非常简洁明了。

So in which corner should you place the diffuser

那现在让咱们看看， 到底在哪个角落放聚光灯

to flood the vampire lair with sunlight?

才能成功杀死吸血鬼呢？

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

如果你想自己思考答案， 可以现在暂停视频。

Answer in 2

离答案公布还有：2秒。

Answer in 1

1秒。

You could tackle this problem by examining smaller rooms,

想要解决这道题， 可以先看看小一点的房间，

and you’d find a lot of interesting patterns.

然后你会发现一些有意思的规律。

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

有一个秘诀可以让你 迅速解决这道难题。

Let’s draw the chamber on a coordinate grid,

让我们先把这个大堂 按比例画在图纸上，

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

把西南角的坐标定为（0，0）

The light passes through grid points

这束阳光的轨迹射入的 坐标点都有一个共性：

with coordinates that are either both even or both odd.

两坐标要么都是偶数， 要么都是奇数。

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

即使这束光经过不同的墙壁 反射后也还是如此。

Another way of thinking about it is this:

换种方法解释，就是说：

since the light travels at a 45 degree angle,

因为这束光是以45度角折射进入的，

it always crosses the diagonal of a unit square.

所以它只会沿着每一个方格的对角线走，

Traveling 1 meter horizontally changes the x coordinate

横着移动1米等于在x轴上移一格，

from even to odd or vice versa.

把偶数变成奇数，或者相反。

Traveling 1 meter vertically changes the y coordinate

竖着移动1米等于在y轴上移一格，

from even to odd or vice versa.

把偶数变成奇数，或者相反。

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

沿着对角线走就是横竖都移动，

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

所以，这束光经过的任何一点，

must be both even, or both odd.

一定是两坐标全是偶数， 或者两坐标全是奇数。

This observation is more powerful than it seems.

这就是我们解决这道题的关键。

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

也就是说，我们找到了一个规律来区分

the light won’t ever go through

光会经过的点和不会经过的点。

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

如果一个点一个坐标是偶数，另一坐标是奇数

the light will miss them.

那么光就不会经过。

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

如此可以看出，这束光不会打到大堂的上两角

since those points have one even and one odd coordinate.

因为这两个角的横纵坐标奇偶不同。

The Southeast corner is the only option for the diffuser.

也就是说，东南角是唯一 可以放聚光灯的地方。

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

果然，当那束宝贵的阳光 打进大堂的时候，

it bounces between the walls

它沿着四壁折射，

and strikes the Southeast corner, spot on.

最后集中了东南角的聚光灯！

The vampires, sensing the intrusion,

这时，吸血鬼们发现了有入侵者，

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

他们从棺材里爬出来， 但是被阳光化为灰烬。

It was a “high stakes” test,

这是一道“高风险”的问题，

and you passed with flying colors.

恭喜你顺利过关！