Can you solve the control room riddle? - Dennis Shasha

譯者: Jessica Lee 審譯者: Max Chern

As your country's top spy,

身為一個國家頂尖的間諜，

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.

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

你能想出控制房是在哪一個樓層嗎？

Pause now to solve the riddle yourself.

先暫停一下自己來解這個謎，

Answer in: 3

三秒後揭曉

Answer in: 2

二秒後揭曉

Answer in: 1

一秒後揭曉

To solve this problem, we need to visualize it.

解決這個問題我們需要想像一下。

For starters, we know that on the correct floor

首先，我們知道對的樓層 有一間房間我們叫 A 房，

there's one room,

let's call it room A,

with one door to the control panel room,

它有一個門通到控制房，

plus one door to room B,

還有一個門去 B 房，

and one to C.

和一個門去 C 房，

So there must be at least four rooms,

所以至少會有四個房間。

which we can represent as circles,

我們可以用圓圈來表示，

drawing lines between them for the doorways.

它們之間畫線來表示門口。

But once we connect rooms B and C,

一旦我們連接 B 房與 C 房，

there are no other connections possible,

就無法再有另一個連接的可能，

so the fourth floor down from the top is out.

所以從樓頂算下來的第四層被剃除。

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

我們知道控制盤的樓層 必須越高越好，

so let's make our way down the pyramid.

所以我們從金字塔由上往下走。

The fifth highest floor doesn't work either.

第五高的層樓也不行，

We can figure that out by drawing it,

我們可以透過畫圖來了解。

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

為了確認我們沒有漏掉任何的可能，

here's another way.

還有另一個方法。

Every door corresponds to a line in our graph

在我們的圖中每個門都對應一條線，

that makes two rooms into neighbors.

使連接的兩房變成鄰居，

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

所以鄰居最後必須是雙數，

no matter how many connections we make.

不管我們畫多少連接。

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

在第五高的樓層 若需符合我們一開始的條件，

we'd need four rooms with three neighbors each,

那我們需要四個房間 它們各自有三個鄰居，

plus the control panel room with one neighbor,

外加一個控制房只連到一個鄰居，

which makes 13 total neighbors.

所以總共會是十三個鄰居。

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

因為十三是個單數，所以也不可能會是。

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

事實上只要是單數房的樓層 都可以排除。

So let's go one more floor down.

我們再往下一層走，

When we draw out the rooms,

當我們畫出這六個房間時，

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

你瞧，我們可以找到一個合乎答案的組合。

Incidentally, the study of such visual models

順道提一下，這種視覺化模型研究

that show the connections and relationships between different objects

顯示出不同對象之間的連接關係，

is known as graph theory.

我們稱為 圖論 (graph theory)。

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

在一個基本的圖表中， 代表物體的圓稱為 結點 (node)，

while the connecting lines are called edges.

連接線叫作 邊 (edges)。

Researchers studying such graphs ask questions like,

研究這類圖表的人員 會這樣提問題，

"How far is this node from that one?"

「這個結點離那個結點有多遠？」

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

「有最多連結的結點有多少條邊？」

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

「這兩個結點間有路徑嗎， 如果有，是多遠？ 」

Graphs like this are often used to map communication networks,

這種圖表常用來繪出通信網路，

but they can represent almost any kind of network,

但它們幾乎可以代表任何種類的網絡。

from transport connections within a city

從一個城市裡的交通連結，

and social relationships among people,

和人與人之間的社交關係，

to chemical interactions between proteins

到蛋白質之間的化學作用，

or the spread of an epidemic through different locations.

或疫情透過不同地點蔓延。

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

有了這些技巧後 我們返回金字塔，

You avoid the guards and security cameras,

你閃過了警衛與監視器，

infiltrate the sixth floor from the top,

潛入到第六高的樓層，

find the hidden panel,

找到隱藏的控制盤，

pull some conspicuous levers,

拉下顯眼的控制桿，

and send the death ray crashing into the ocean.

將死亡射線墜毀海裡。

Now, time to solve the mystery

現在輪到解開這個謎：

of why your surveillance team always gives you cryptic information.

為什麼你的監控小組 總是給你詭譎的情報？

Hi everybody.

大家好，

If you liked this riddle, try solving these two.

如果你喜歡這個謎題，可以再試試這兩個。

翻譯：Jessica Lee