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

直到，教授不小心 踏入了一個時空入口。

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

你只有一分鐘可以跳進去救他，

and leaves him stranded in history.

一分鐘後入口就會關閉， 把他留在歷史中。

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

一旦你通過了入口，它就會關閉，

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

你唯一能回來的方式 就是創造一個新的入口，

using the chrono-nodules from your lab.

用你實驗室的時間結節 就可以做到。

Activated nodules connect to each other

透過紅或藍色「超光速粒子纏結」， 啟動的結節會彼此連接。

via red or blue tachyon entanglement.

啟動更多的結節，它們就都會 連結到該區域中的其他結節。

Activate more nodules and they'll connect

當以結節為頂點 形成紅或藍色三角形時，

to all other nodules in the area.

就會打開一個穿越時空的門， 帶你回到現今。

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

但每一段連線 呈現的顏色是隨機的，

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

不可能選擇或改變它的顏色。

But the color of each individual connection manifests at random,

還有一個問題：

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

每一個結節都會造成 時間的不穩定，

And there's one more problem:

增加你在通過入口時 入口垮掉的可能性。

each individual nodule creates a temporal instability

所以，能帶越少的結節越好。

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

入口就要關閉了。

So the fewer you bring, the better.

你最少需要帶多少個結節， 才能確保你能創造出

The portal's about to close.

紅色或藍色的三角形， 以回到現今？

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

如果你想要自己解解看， 請在這裡暫停！

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

答案即將公佈：三

Pause here 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

這個問題非常深奧， 有一整個數學分支，

Answer in: 1

叫做拉姆西理論， 是從它發展出來的。

This question is so rich that an entire branch of mathematics

拉姆西理論是許多著名難題的根源。

known as Ramsey Theory developed from it.

這題並不簡單，

Ramsey Theory is home to some famously difficult problems.

但如果你系統性地 去處理它，是能夠解決的。

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

想像你只帶了三個結節。

if you approach it systematically.

那會足夠嗎？不夠——比如，

Imagine you brought just three nodules.

你可能會有兩條藍線 和一條紅線，

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

那你就永遠被困在過去了。

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

帶四個結節夠嗎？不夠——

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

這裡有許多種排法， 並不會產生出藍或紅色三角形。

that don't give a blue or red triangle.

那五個呢？結果發現，

What about five?

有一種連結的排法 並不會產生出藍或紅色三角形。

It turns out there is an arrangement of connections

這些小型的三角形不算數， 因為它們的頂點並不是結節。

that avoids creating a blue or red triangle.

然而，六個結節永遠都能夠

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

創造出一個藍或紅色三角形。

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

這一點不用排列出每種可能情況 就證明出來，方法如下。

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

想像一下，啟動第六個結節，

Imagine activating the sixth nodule,

並思考它可能會如何 與其他五個結節連結。

and consider how it might connect to the other five.

可能的連結方式是這六種之一：

It could do so in one of six ways:

用五條紅色連線、 五條藍色連線

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

或藍線和紅線混合。

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

不論是哪種可能性， 都會有至少三條同色的線，

coming from this nodule.

從這個結節連出來。

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

咱們看看這三條同色線 另一端的結節。

of those same three color connections.

如果這三條是藍線，

If the connections were blue,

在這三個結節中 只要有再一條藍線，

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

就會產生出藍色三角形。

So the only way we could get in trouble

所以，唯一可能出錯的狀況，

is if all the connections between them were red.

是如果它們之間 所有的連線都是紅線。

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

但那三條紅線 就會產生一個紅色三角形。

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

不論發生哪種狀況， 都會得到紅或藍色三角形，

and open our doorway.

打開我們的時空之門。

On the other hand,

另一方面，如果原本的 三條連線都是紅線，

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

而非藍色，同樣的論點仍然適用，

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

只是顏色對調而已。

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

換言之，不論這些連線是什麼顏色，

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

只要有六個結節，就一定會 創造出紅或藍色三角形，

So you grab six nodules and jump through the portal.

開啟回家的門。

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

所以，你抓了六個結節 便跳進入口。

Turns out, that didn't take much time.

你希望你的實習能帶給你 可貴的人生體驗，