Can you solve the Ragnarok riddle? - Dan Finkel

譯者: Lilian Chiu 審譯者: Helen Chang

Ragnarok. The fabled end of the world,

諸神黃昏。傳說中的世界末日，

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

巨人、怪獸、北歐諸神 為了未來而戰。

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

諸神很輕易就佔了上風， 直到巨大海蛇耶夢加得出現。

It swallowed Valhalla, contorted itself across the land,

牠吞掉了瓦爾哈拉， 盤在整片大地上，

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

接著融合成了連接在一起的身體，

沒有頭也沒有尾。

As it begins to digest Valhalla,

當牠開始消化瓦爾哈拉，

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

筋疲力竭的奧丁解釋說 他還有剛好足夠的力量

可以做最後一次雷擊， 攻擊這個生物。

with one final bolt of lightning.

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

如果你用傳說中的雷神之鎚 妙爾尼爾將他的攻擊放大，

it should pierce the massive serpent.

應該就足以貫穿這條大蛇。

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

你要用超快的速度 沿著大蛇的身體奔跑。

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

當你舉高鎚子時， 奧丁就會用雷擊攻擊它，

and split Jörmungandr open at that point.

在那個點將耶夢加得的身體切開。

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

接著，你得要持續 沿著大蛇的身體奔跑，

until every part of it is destroyed.

直到牠的每一部分都被摧毀。

You can’t run over the same section twice

你不能經過同樣的區段兩次，

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

要不然你就會掉進已經 被擊毀的部分蛇體中。

But you can make multiple passes through points where the creature

但你可以多次通過蛇體

intersects its own body.

相疊的交叉點。

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

只要有一部分沒有摧毀， 耶夢加得就會用魔法再生，

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

奧丁最後的力量已經用盡， 瓦爾哈拉就會永遠滅亡。

What path can you take to destroy the serpent?

你要走什麼路徑來摧毀這條大蛇？

Pause now to figure it out yourself!

若要嘗試解題，在此暫停。

Answer in 3

答案即將公佈：三、

2

二、

1

一

One powerful way to solve problems is to simplify.

要解決問題，一個 很有效的方法就是簡化。

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

在這個例子中， 我們可以把焦點放在

對路徑選擇很重要的兩樣東西上，

that are important for our path:

intersections and the stretches of snake between them.

交叉點和交叉點間的伸長蛇體。

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

在圖論中，則是稱為節點和邊緣。

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

邊緣很重要，因為邊緣 是我們要走的路線。

And the nodes matter because they connect the edges,

節點很重要，因為節點銜接邊緣，

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

且我們要在節點上做決擇， 決定要跑向哪一條邊緣。

This simplification into nodes and edges leaves us

把問題簡化成節點和邊緣， 就讓我們得到了一個

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

普遍且重要的數學物元：

圖，或稱網路。

or network.

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

我們只需要解出數學家 所謂的歐拉路徑，

which traces every edge exactly once.

也就是剛好把每個邊緣 都走一次的路徑。

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

別急著把路徑視為一個整體， 咱們先放大看單一個節點。

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

在你奔跑的某個時點，你會 進入那個節點，接著再離開它。

That takes care of two edges.

那就處理掉了兩條邊緣。

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

如果你再次進入該節點， 你就得再次離開，

which requires another pair of edges.

那就需要有另一對邊緣。

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

所以路徑上的每個節點 都必須要有成對的邊緣。

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

一對邊緣中的一條邊緣用來進入，

另一條用來離開。

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

那就表示每個節點必須要 連結到偶數條邊緣。

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

有兩個例外，起點和終點，

where you can exit without entering, or vice versa.

在這兩個點，可以 只進不出或只出不進。

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

我們再次回去看大蛇形成的網路，

and number how many edges emerge from each node,

計算每個節點連結了幾個邊緣，

a pattern jumps out that fits what we just saw.

就會出現一個模式， 符合我們剛才看到的。

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

每個節點都連結到偶數條 邊緣，只有兩個例外。

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

因此，這兩個點其中之一必須要是 路徑的起點，另一個是終點。

Interestingly enough, any connected network that has exactly 2 nodes

有趣的是，如果一個連結網路

剛好只有兩個節點 連結到奇數條邊緣，

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

該網路中就一定會有 一條歐拉路徑。

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

如果網路中所有節點都連結到 偶數條邊緣，亦會是如此——

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

在這種情況中， 起點和終點會是同一點。

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

知道這些之後， 咱們回來看看完整的全圖。

We can begin by taking care of this edge here.

我們可以從處理這條邊緣開始。

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

現在我們可以在整條蛇 身上曲折來回，

until we reach the end.

直到抵達終點。

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

這只是一種解決方案—— 系統化是有幫助的，

but you’re likely to happen upon many others

但一旦你知道從何開始和結束，

once you know where to begin and end your run.

你很可能會再發現 許多其他解決方案。

You hold your hammer high at the opportune moment,

在恰當的時刻，你高舉你的鎚子，

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

奧丁向你放出一波 拯救世界的雷擊。

Then you run like you’ve never run before.

接著你死命地奔跑。

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

如果你成功了，那肯定沒有什麼 能阻止北歐諸神的神威。

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

若還有像那樣的生物 想要接近你……

well, that would be a story for another day.

嗯，那就是下回的故事了。