Can you solve the control room riddle? - Dennis Shasha

翻译人员: Cissy Yun 校对人员: Mingyu Cui

As your country's top spy,

作为国家的顶级间谍，

you must infiltrate the headquarters of the evil syndicate,

你必须潜入邪恶组织的总部，

find the secret control panel,

找到隐蔽的控制板，

and deactivate their death ray.

并且关闭死亡射线。

But all you have to go on is the following information

但是你拥有的信息只是

picked up by your surveillance team.

你的监督团队所收集的。如下：

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

这个总部是一个巨大的金字塔 在顶层有一个的房间，

two rooms on the next,

下面一层有两间房间，

and so on.

以此类推。

The control panel is hidden behind a painting

控制板被藏在一幅画的后面

on the highest floor that can satisfy the following conditions:

这幅画在满足下面的这些条件的最高层：

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

在每一层，每一个房间恰好有三张门通往其他房间，

except the control panel room,

除了控制室

which connects to only one,

只连接一个房间。

there are no hallways,

没有走廊，

and you can ignore stairs.

忽略楼梯。

Unfortunately, you don't have a floor plan,

不幸的是，你没有楼层平面图，

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

而且你仅有足够时间在警报系统恢复正常之前

before the alarm system reactivates.

完整搜寻某一层。

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

你能想出控制室在哪一层吗？

Pause now to solve the riddle yourself.

现在暂停，尝试解决这个谜题。

Answer in: 3

答案在3秒后

Answer in: 2

答案在2秒后

Answer in: 1

答案在1秒后

To solve this problem, we need to visualize it.

为了解决这个问题，我们需要把它形象化。

For starters, we know that on the correct floor

最开始，我们知道在每一个楼层

there's one room,

都至少有一个房间，

let's call it room A,

我们把它叫做房间A，

with one door to the control panel room,

有一个门通往控制室

plus one door to room B,

另一个门通往房间B，

and one to C.

还有一个通往房间C。

So there must be at least four rooms,

所以这至少有4个房间，

which we can represent as circles,

我们可以把它们绘成圆形，

drawing lines between them for the doorways.

在它们的门之间连线。

But once we connect rooms B and C,

但是一旦我们连接B和C，

there are no other connections possible,

就没有其他可能的连接了，

so the fourth floor down from the top is out.

所以第4层楼不满足条件。

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

我们知道控制室必须尽可能的高，

so let's make our way down the pyramid.

所以我们继续下金字塔。

The fifth highest floor doesn't work either.

第5层也不满足条件。

We can figure that out by drawing it,

我们可以通过画图得出这个结论，

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

但是为了确保我们没有错失任何的可能，

here's another way.

还有另外一种方法。

Every door corresponds to a line in our graph

在我们的图中，每一个门对应一条线

that makes two rooms into neighbors.

使两个房间相邻。

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

所以最后必须是有偶数倍的相邻房间，

no matter how many connections we make.

无论我们连了多少线。

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

到了第5层，为了满足我们刚开始的条件，

we'd need four rooms with three neighbors each,

我们需要4个房间，每个房间都有3个相邻的房间，

plus the control panel room with one neighbor,

加上控制室有1个相邻的房间，

which makes 13 total neighbors.

总共就有13个相邻的房间了。

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

因为这是一个奇数，这是不可能出现的，

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

实际上，这样就排除了有奇数个房间的所有层。

So let's go one more floor down.

所以让我们再往下一层。

When we draw out the rooms,

当我们画出房间的时候，

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

看，我们可以找到这样一种可行的安排。

Incidentally, the study of such visual models

顺便说一句，这种可视化模型的

that show the connections and relationships between different objects

表明不同物体间的联系和关系的研究

is known as graph theory.

叫做图论。

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

在一个基本的图中，每一个表示物体的圆叫一个节点，

while the connecting lines are called edges.

而相连的线被称为边。

Researchers studying such graphs ask questions like,

研究人员研究这样的图时会这样问，

"How far is this node from that one?"

“这个节点和另外一个之间有多远？”

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

“一个节点最多有多少边与它相连？”

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

“这两个节点之间有没有一条路线，如果有，有多长？”

Graphs like this are often used to map communication networks,

这样的图表经常被用作绘制通讯网，

but they can represent almost any kind of network,

但是它们几乎可以呈现任何种类的网，

from transport connections within a city

从一个城市的交通网，

and social relationships among people,

人与人的社交关系网，

to chemical interactions between proteins

到蛋白质之间的化学作用

or the spread of an epidemic through different locations.

或者是通过不同地区的传染病的传播。

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

所以，有了这些技术，回到金字塔上。

You avoid the guards and security cameras,

你躲开了侍卫个安保的摄像机，

infiltrate the sixth floor from the top,

从顶层潜入第六层，

find the hidden panel,

找到了隐蔽的控制板，

pull some conspicuous levers,

拉了几个杠杆，

and send the death ray crashing into the ocean.

把死亡射线偏折到了大海里。

Now, time to solve the mystery

现在，到了解开这个谜的时候了：

of why your surveillance team always gives you cryptic information.

为什么你的监督团队总是给你一些加了密的信息呢？

Hi everybody.

嗨！

If you liked this riddle, try solving these two.

如果你喜欢这个谜语，也尝试解开这两个吧。