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  • 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.

    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.

As your country's top spy,

身為一個國家頂尖的間諜,

字幕與單字

影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

B1 中級 中文 TED-Ed 樓層 房間 鄰居 金字塔 圖表

【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)

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    黃于珍 發佈於 2021 年 01 月 14 日
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