Can you solve the time travel riddle? - Dan Finkel

翻译人员: Zhenlan Yao 校对人员: Liu Qi

Your internship in Professor Ramsey’s physics lab has been amazing.

你在拉姆齐教授物理实验室的 实习工作一直以来都非常棒，

Until, that is, the professor accidentally stepped through a time portal.

直到教授不小心穿过了时间传送门。

You’ve got just a minute to jump through the portal to save him before it closes

在传送门关闭、将教授 困在历史时空之前，

and leaves him stranded in history.

你有一分钟的时间 穿过传送门拯救他。

Once you’re through it, the portal will close,

当你进入传送门之后， 传送门会关闭，

and your only way back will be to create a new one

返回当前时空的唯一办法是

利用实验室里的“时间结节” 建立一个新的传送门。

using the chrono-nodules from your lab.

Activated nodules connect to each other

激活后的结节会互相连接，

via red or blue tachyon entanglement.

通过红色或蓝色超光速粒子缠结。

Activate more nodules and they’ll connect

更多结节激活后，

to all other nodules in the area.

它们将会与区域内其他结节相互连接。

As soon as a red or blue triangle is created with a nodule at each point,

一旦形成一个以结节为顶点的 蓝色或红色三角形时，

it opens a doorway through time that will take you back to the present.

时空之门即可打开， 将你带回当前时空。

But the color of each individual connection manifests at random,

但每次连接的颜色随机出现，

and there’s no way to choose or change its color.

无法选择或者改变连接的颜色。

And there’s one more problem:

还有一个问题是：

each individual nodule creates a temporal instability

每个结节都会降低 时空稳定性，

that raises the chances the portal might collapse as you go through it.

增加穿越时传送门崩溃的风险。

So the fewer you bring, the better.

所以携带的时间结节越少越好。

The portal’s about to close.

传送门即将关闭。

What’s the minimum number of nodules you need to bring

最少需要带多少个结节

to be certain you’ll create a red or blue triangle and get back to the present?

才能保证可以组成一个红色或 蓝色三角形，回当前时空呢？

Pause here if you want to figure it out for yourself!

(想要自行计算可以在此处暂停)

Answer in: 3

（答案将在三秒后揭晓）3

Answer in: 2

2

Answer in: 1

1

This question is so rich that an entire branch of mathematics

这个问题内涵丰富，

知名的拉姆齐理论的整个 数学分支都由此发展而来。

known as Ramsey Theory developed from it.

Ramsey Theory is home to some famously difficult problems.

拉姆齐理论包含了许多著名难题。

This one isn’t easy, but it can be handled

本题虽不简单， 但通过系统性地分析，

if you approach it systematically.

还是可以解决的。

Imagine you brought just three nodules.

假设只带三个结节，

Would that be enough? No - for example, you might have two blue

三个够吗？不够。举个例子， 可能会出现两蓝一红的连接，

and one red connection, and be stuck in the past forever.

那么你会被永远地困在过去。

Would four nodules be enough? No - there are many arrangements here

四个够不够？不够。 因为存在多种排列方式

that don’t give a blue or red triangle.

可以使蓝色或红色三角不成立。

What about five?

那么五个呢？

It turns out there is an arrangement of connections

还是会有一种排列方式，

that avoids creating a blue or red triangle.

会使蓝色或红色三角不成立。

These smaller triangles don’t count because they don’t have a nodule at each corner.

中间这些小三角形不算， 因为它们的各顶点不是结节。

However, six nodules will always create a blue triangle or a red triangle.

但是，六个结节将始终可以构成 蓝色或红色三角形。

Here’s how we can prove that without sorting through every possible case.

下面是不用排除法， 我们证明这个结论的方法。

Imagine activating the sixth nodule,

试想，激活第六个结节时，

and consider how it might connect to the other five.

它将如何与其它五个连接。

It could do so in one of six ways:

一定会是下列六种情况中的一种：

with five red connections, five blue connections, or some mix of red and blue.

五红，五蓝，或红蓝混合。

Notice that every possibility has at least three connections of the same color

可以发现，所有可能性中

该结节的连接至少有三个是同色的。

coming from this nodule.

Let’s look at just the nodules on the other end

只看这三条同色连接的

of those same three color connections.

另一端的结节，

If the connections were blue,

如果连接为蓝色线，

then any additional blue connection between those three would give us a blue triangle.

那么在这三个结节之间任意位置 添加蓝色连接都会构成蓝色三角形。

So the only way we could get in trouble

所以唯一会让我们遇到麻烦的情形是，

is if all the connections between them were red.

结节间的连接全部是红色。

But those three red connections would give us a red triangle.

但是三个红色连接将会 构成一个红色三角形。

No matter what happens, we’ll get a red or a blue triangle,

无论怎样，我们都会得到 一个红色或蓝色三角形，

and open our doorway.

打开传送门。

On the other hand,

另一方面，

if the original three connections were all red instead of blue,

如果原来的三个连接 均为红色，而非蓝色，

the same argument still works, with all the colors flipped.

所有颜色翻个样， 同样的结论依然成立。

In other words, no matter how the connections are colored,

换句话说，不论连接是什么颜色，

six nodules will always create a red or blue triangle and a doorway leading home.

六个结节始终能组成一个红色或 蓝色三角，打开回家的大门。

So you grab six nodules and jump through the portal.

所以带上六个结节， 跳进传送门吧。

You were hoping your internship would give you valuable life experience.

你所期待的实习期 带给你宝贵的人生经历，

Turns out, that didn’t take much time.

其实并不需要花费太长时间。