Name: 【TED-Ed】你能解開控制室的謎題嗎？- 丹尼斯-沙沙 (【TED-Ed】Can you solve the control room riddle? - Dennis Shasha)
Uploaded: 2021-01-14T06:19:10.000Z
Duration: 4 min 1 s

情態助動詞 B1

you must infiltrate the headquarters of the evil syndicate,

But all you have to go on  is the following information

但你僅有以下情報 來繼續你的任務，

The headquarters is a massive pyramid with a single room at the top level,

總部是一個龐大的金字塔， 頂層有個單間房，

The control panel is hidden behind a painting

on the highest floor that can satisfy the following conditions:

並在符合下列條件的最高樓層中：

Each room has exactly three doors to other rooms on that floor,

每間房間有三個門 通到同樓層的不同房間，

Unfortunately,  you don't have a floor plan,

and you'll only have enough time to search a single floor

在警報系統恢復前， 你只有足夠的時間搜尋一層樓。

你能想出控制房是在哪一個樓層嗎？

Can you figure out which floor the control room is on?

解決這個問題我們需要想像一下。

To solve this problem,  we need to visualize it.

首先，我們知道對的樓層 有一間房間我們叫 A 房，

For starters, we know  that on the correct floor

就無法再有另一個連接的可能，

drawing lines between them for the doorways.

所以從樓頂算下來的第四層被剃除。

我們知道控制盤的樓層 必須越高越好，

所以我們從金字塔由上往下走。

so the fourth floor down  from the top is out.

We know the control panel has to be as high up as possible,

為了確認我們沒有漏掉任何的可能，

The fifth highest floor  doesn't work either.

在我們的圖中每個門都對應一條線，

but to be sure we haven't missed any possibilities,

Every door corresponds to a line in our graph

在第五高的樓層 若需符合我們一開始的條件，

So in the end, there have to be an even number of neighbors

那我們需要四個房間 它們各自有三個鄰居，

外加一個控制房只連到一個鄰居，

On the fifth highest floor, to fulfill our starting conditions,

we'd need four rooms  with three neighbors each,

因為十三是個單數，所以也不可能會是。

plus the control panel room with one neighbor,

事實上只要是單數房的樓層 都可以排除。

Since that's an odd number, it's not possible,

and, in fact, this also rules out every floor that has an odd number of rooms.

你瞧，我們可以找到一個合乎答案的組合。

順道提一下，這種視覺化模型研究

顯示出不同對象之間的連接關係，

low and behold, we can find an arrangement that works like this.

Incidentally, the study  of such visual models

在一個基本的圖表中， 代表物體的圓稱為 結點 (node)，

that show the connections and relationships between different objects

研究這類圖表的人員 會這樣提問題，

In a basic graph, the circles representing the objects are known as nodes,

「這個結點離那個結點有多遠？」

while the connecting lines  are called edges.

「有最多連結的結點有多少條邊？」

Researchers studying such graphs ask questions like,

「這兩個結點間有路徑嗎， 如果有，是多遠？ 」

這種圖表常用來繪出通信網路，

"How many edges does  the most popular node have?"

但它們幾乎可以代表任何種類的網絡。

"Is there a route between these two nodes, and if so, how long is it?"

Graphs like this are often used to map communication networks,

but they can represent almost any kind of network,

有了這些技巧後 我們返回金字塔，

to chemical interactions between proteins

or the spread of an epidemic through different locations.

So, armed with these techniques, back to the pyramid.

You avoid the guards and security cameras,

為什麼你的監控小組 總是給你詭譎的情報？

and send the death ray crashing into the ocean.

如果你喜歡這個謎題，可以再試試這兩個。

of why your surveillance team always gives you cryptic information.

If you liked this riddle,  try solving these two.