Can you solve the Ragnarok riddle? - Dan Finkel

翻译人员: Wanting Zhong 校对人员: Yanyan Hong

Ragnarok. The fabled end of the world,

诸神黄昏（Ragnarok）。 传说中的世界末日。

when giants, monsters, and Norse gods battle for the future.

巨人、怪物和北欧诸神 为了未来而战。

The gods were winning handily until the great serpent Jörmungandr emerged.

众神胜券在握，直到巨蛇 耶梦加得（Jörmungandr）现身。

It swallowed Valhalla, contorted itself across the land,

它吞掉了英灵神殿瓦尔哈拉（Valhalla）， 用身体盘绕着大地，

and then merged into one continuous body with no head and no tail.

化为了一具连绵不绝、 无头无尾的躯体。

As it begins to digest Valhalla,

当巨蛇开始消化瓦尔哈拉时，

an exhausted Odin explains that he has just enough power to strike the creature

筋疲力竭的众神之王 奥丁（Odin）解释说，

他只剩下朝那怪物 击出最后一道闪电的力气了。

with one final bolt of lightning.

If you magnify his blast with your fabled hammer, Mjölnir,

如果用你举世闻名的雷神之锤 （Mjölnir）将他的闪电攻击增倍，

it should pierce the massive serpent.

应该就足以贯穿巨蟒的身体。

You’ll run with super-speed along the serpent’s body.

你可以用超人的速度沿着蛇身疾驰。

When you hold your hammer high, Odin will strike it with lightning

当你高高举起锤子时， 奥丁就会朝它掷出闪电，

and split Jörmungandr open at that point.

将耶梦加得从那一处劈开。

Then, you’ll need to continue running along its body

然后，你要继续沿着巨蛇的身体奔跑，

until every part of it is destroyed.

直到将它的每一寸都摧毁。

You can’t run over the same section twice

你不能重复踏过同一段区域，

or you’ll fall into the already blasted part of the snake.

否则你会掉入巨蛇 已经劈裂的身体中。

But you can make multiple passes through points where the creature

但你可以反复经过

巨蛇自身相互交错的节点。

intersects its own body.

If you leave any portion un-zapped, Jörmungandr will magically regenerate,

如果漏过任何一处未加电灼， 耶梦加得就会藉由魔力重生，

Odin’s last power will be spent, and Valhalla will fall forever.

奥丁将耗尽最后的力量， 瓦尔哈拉也将堕入永恒的黑暗。

What path can you take to destroy the serpent?

你该选择怎样的路径 才能彻底摧毁巨蛇呢？

Pause now to figure it out yourself!

暂停视频，试着解答吧！

Answer in 3

答案将在 3 秒后公布

2

2 秒

1

1 秒

One powerful way to solve problems is to simplify.

要解决问题， 一种有效方法是进行简化。

And in this case, we can focus our attention on the two things

在这个问题中， 我们可以着重关注

对于要寻找的路径相当重要的两点：

that are important for our path:

intersections and the stretches of snake between them.

交叉点，以及交点之间的 “蛇身” 。

Or, as they’re referred to in graph theory, nodes and edges.

在图论中，它们分别被称作 “节点（node）” 和 “边（edge）” 。

The edges are important because they’re what we need to travel.

边很重要，因为我们要走的就是边。

And the nodes matter because they connect the edges,

而顶点也不可小觑， 因为边与边是通过节点相连的，

and are where we may need to make choices as we run from edge to edge.

而且当我们决定要跑向哪一条边时， 我们需要在节点处做出决定。

This simplification into nodes and edges leaves us

将问题简化成节点与边， 我们就得到了

with a ubiquitous and important mathematical object known as a graph,

一个无处不在的重要的 数学对象，叫做 “图（graph）”，

or network.

或者 “网（network）”。

We just need to figure out how to travel what mathematicians call an Eulerian path,

我们只需要找出一条数学家所说的 “欧拉路径（Eulerian path）”，

which traces every edge exactly once.

将每条边恰好走一次 （即一笔画问题）。

Instead of looking at the path as a whole, let’s zoom in on a single node.

我们先不去看整体的路径， 而是放大到一个节点上。

During some moment in your run, you’ll enter that node, and then exit it.

在你奔跑途中的某一刻， 你会进入这个节点，然后离开。

That takes care of two edges.

这就让你经过了两条边。

If you enter again, you’ll need to exit again too,

如果你再次进入这个节点， 你也必须再离开一次，

which requires another pair of edges.

这就需要经过另一对边。

So every point along your path will have edges that come in pairs.

因此，你的路径中的每一个点 都会有成对的边。

One edge in each pair will function as entrance; the other as exit.

每对中的一条边是“入点”， 另一条边则是“出点”。

And that means that the number of edges coming out of every node must be even.

这也意味着从每个节点 出来的边数必须是偶数。

There are just two exceptions: the start and end points,

只有两个例外：起点和终点，

where you can exit without entering, or vice versa.

你可以只离开不进入， 也可以只进入不离开。

If we look at the network formed by the serpent again,

如果我们再看看由巨蛇形成的网，

and number how many edges emerge from each node,

并数数从每个节点发出了多少条边，

a pattern jumps out that fits what we just saw.

一个与刚刚所见 相符的图案便跃然而出。

Every node has an even number of edges emerging from it, except two.

除了两个节点，其它每个节点 所连接的边数都是偶数，

So one of these must be the start of your route, and the other the end.

这两个例外中的一个肯定是起点， 另一个肯定是终点。

Interestingly enough, any connected network that has exactly 2 nodes

有意思的是，任何一个连通图 如果恰好有两个节点具有奇数条边，

with an odd number of edges will also contain an Eulerian path.

那么这个连通图肯定可以被一笔画。

The same is true if there are no nodes with an odd number of edges—

如果图中没有节点连接了奇数条边， 这个图同样能被一笔画——

in that case the path starts and ends in the same spot.

这种情况下，欧拉路径 将在同一个点开始并结束。

So knowing that, let’s return to our full graph.

知道这些之后，让我们回到完整的图。

We can begin by taking care of this edge here.

我们可以先途经这条边，

Now we can zig-zag back and forth across the whole snake

然后就可以按 “之” 字形 来回绕完整条蛇，

until we reach the end.

直到抵达终点。

And that's just one solution— it helps to be systematic,

这只是一种解法—— 保持条理性会让一笔画更容易，

but you’re likely to happen upon many others

但只要知道了路径的起点和终点，

once you know where to begin and end your run.

你或许能发现许多条可行的路径。

You hold your hammer high at the opportune moment,

你抓准时机，将锤子高高举起，

and Odin sends the world-saving surge of lightning at you.

奥丁便将拯救世界的 一道闪电朝你掷来。

Then you run like you’ve never run before.

然后你就拼了老命地撒腿狂奔，

If you can pull this off, surely nothing could stop the might of the Norse Gods.

如果你能成功，想必再无他物 能阻止北欧众神的威势。

And if something like that were out there, slouching its way towards you…

而假如还有像那样的家伙 慢悠悠地拖着步子朝你走来……

well, that would be a story for another day.

嗯，那就是后话了。