you must infiltrate the headquarters of the evil syndicate,

你須要潛入邪惡集團總部，

find the secret control panel,

找到那機密的控制盤，

and deactivate their death ray.

然後解除他們的死亡射線。

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，

picked up by your surveillance team.

這是監控小組所收集來的。

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，

two rooms on the next,

下一個樓層是兩間房，

and so on.

以此類推。

The control panel is hidden behind a painting

控制盤藏在一幅畫的後面，

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，

except the control panel room,

除了控制房，

which connects to only one,

它只連到一個房間，

there are no hallways,

沒有走廊，

and you can ignore stairs.

也不用考慮樓梯。

Unfortunately, you don't have a floor plan,

很不幸的是你沒有平面圖，

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。

before the alarm system reactivates.

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?

先暫停一下自己來解這個謎，

Pause now to solve the riddle yourself.

三秒後揭曉

Answer in: 3

二秒後揭曉

Answer in: 2

一秒後揭曉

Answer in: 1

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

它有一個門通到控制房，

there's one room,

還有一個門去 B 房，

let's call it room A,

和一個門去 C 房，

with one door to the control panel room,

所以至少會有四個房間。

plus one door to room B,

我們可以用圓圈來表示，

and one to C.

它們之間畫線來表示門口。

So there must be at least four rooms,

一旦我們連接 B 房與 C 房，

which we can represent as circles,

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。

But once we connect rooms B and C,

我們知道控制盤的樓層 必須越高越好，

there are no other connections possible,

所以我們從金字塔由上往下走。

so the fourth floor down from the top is out.

第五高的層樓也不行，

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

我們可以透過畫圖來了解。

so let's make our way down the pyramid.

為了確認我們沒有漏掉任何的可能，

The fifth highest floor doesn't work either.

還有另一個方法。

We can figure that out by drawing it,

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,

使連接的兩房變成鄰居，

here's another way.

所以鄰居最後必須是雙數，

Every door corresponds to a line in our graph

不管我們畫多少連接。

that makes two rooms into neighbors.

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，

no matter how many connections we make.

外加一個控制房只連到一個鄰居，

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

所以總共會是十三個鄰居。

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。

which makes 13 total neighbors.

我們再往下一層走，

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

當我們畫出這六個房間時，

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。

So let's go one more floor down.

順道提一下，這種視覺化模型研究

When we draw out the rooms,

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.

我們稱為 圖論 (graph theory)。

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

連接線叫作 邊 (edges)。

is known as graph theory.

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？ 」

"How far is this node from that one?"

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?"

從一個城市裡的交通連結，

Graphs like this are often used to map communication networks,

和人與人之間的社交關係，

but they can represent almost any kind of network,

到蛋白質之間的化學作用，

from transport connections within a city

或疫情透過不同地點蔓延。

and social relationships among people,

有了這些技巧後 我們返回金字塔，

to chemical interactions between proteins

你閃過了警衛與監視器，

or the spread of an epidemic through different locations.

潛入到第六高的樓層，

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

找到隱藏的控制盤，

You avoid the guards and security cameras,

拉下顯眼的控制桿，

infiltrate the sixth floor from the top,

將死亡射線墜毀海裡。

find the hidden panel,

現在輪到解開這個謎：

pull some conspicuous levers,

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.

大家好，

Now, time to solve the mystery

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.

翻譯：Jessica Lee

Hi everybody.

If you liked this riddle, try solving these two.