Can you solve the Ragnarok riddle

你能解決諸神黃昏之謎嗎

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Ragnarok.?

The fabled end of the world, when giants, monsters, and Norse gods battle for the future.

The gods were winning handily until the great serpent J?rmungandr emerged.?

It swallowed Valhalla, contorted itself across the land, and then merged into one continuous body with no head and no tail.?

As it begins to digest Valhalla, an exhausted Odin explains that he has just enough power to strike the creature with one final bolt of lightning.

諸神黃昏（Ragnarok）。?

傳說中的世界末日。巨人、怪物和北歐諸神 為了未來而戰(zhàn)。

眾神勝券在握，直到巨蛇 耶夢(mèng)加得（J?rmungandr）現(xiàn)身。

它吞掉了英靈神殿瓦爾哈拉（Valhalla）， 用身體盤繞著大地，化為了一具連綿不絕、 無頭無尾的軀體。

當(dāng)巨蛇開始消化瓦爾哈拉時(shí)，筋疲力竭的眾神之王 奧?。∣din）解釋說，他只剩下朝那怪物 擊出最后一道閃電的力氣了。

If you magnify his blast with your fabled hammer, Mj?lnir, it should pierce the massive serpent.?

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

When you hold your hammer high, Odin will strike it with lightning and split J?rmungandr open at that point.?

Then, you’ll need to continue running along its body until every part of it is destroyed.?

You can’t run over the same section twice or you’ll fall into the already blasted part of the snake.?

But you can make multiple passes through points where the creature intersects its own body.

如果用你舉世聞名的雷神之錘 （Mj?lnir）將他的閃電攻擊增倍，應(yīng)該就足以貫穿巨蟒的身體。

你可以用超人的速度沿著蛇身疾馳。

當(dāng)你高高舉起錘子時(shí)， 奧丁就會(huì)朝它擲出閃電，將耶夢(mèng)加得從那一處劈開。

然后，你要繼續(xù)沿著巨蛇的身體奔跑，直到將它的每一寸都摧毀。

你不能重復(fù)踏過同一段區(qū)域，否則你會(huì)掉入巨蛇 已經(jīng)劈裂的身體中。

但你可以反復(fù)經(jīng)過巨蛇自身相互交錯(cuò)的節(jié)點(diǎn)。

If you leave any portion un-zapped, J?rmungandr will magically regenerate, Odin’s last power will be spent, and Valhalla will fall forever.?

What path can you take to destroy the serpent??

Pause now to figure it out yourself!?

Answer in 3 2 1

如果漏過任何一處未加電灼， 耶夢(mèng)加得就會(huì)藉由魔力重生，奧丁將耗盡最后的力量， 瓦爾哈拉也將墮入永恒的黑暗。

你該選擇怎樣的路徑 才能徹底摧毀巨蛇呢？

暫停視頻，試著解答吧！

答案將在?3?秒后公布

答案將在2?秒后公布

答案將在1?秒后公布

One powerful way to solve problems is to simplify.?

And in this case, we can focus our attention on the two things that are important for our path: intersections and the stretches of snake between them.?

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

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

And the nodes matter because they connect the edges, and are where we may need to make choices as we run from edge to edge.

要解決問題， 一種有效方法是進(jìn)行簡化。

在這個(gè)問題中， 我們可以著重關(guān)注對(duì)于要尋找的路徑相當(dāng)重要的兩點(diǎn)：交叉點(diǎn)，以及交點(diǎn)之間的?“蛇身”?。

在圖論中，它們分別被稱作?“節(jié)點(diǎn)（node）”?和?“邊（edge）”?。

邊很重要，因?yàn)槲覀円叩木褪沁叀?/p>

而頂點(diǎn)也不可小覷， 因?yàn)檫吪c邊是通過節(jié)點(diǎn)相連的，而且當(dāng)我們決定要跑向哪一條邊時(shí)， 我們需要在節(jié)點(diǎn)處做出決定。

This simplification into nodes and edges leaves us with a ubiquitous and important mathematical object known as a graph, or network.?

We just need to figure out how to travel what mathematicians call an Eulerian path, which traces every edge exactly once.?

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

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

That takes care of two edges.

?If you enter again, you’ll need to exit again too, which requires another pair of edges.?

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

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

將問題簡化成節(jié)點(diǎn)與邊， 我們就得到了一個(gè)無處不在的重要的 數(shù)學(xué)對(duì)象，叫做?“圖（graph）”，或者?“網(wǎng)（network）”。

我們只需要找出一條數(shù)學(xué)家所說的?“歐拉路徑（Eulerian path）”，將每條邊恰好走一次 （即一筆畫問題）。

我們先不去看整體的路徑， 而是放大到一個(gè)節(jié)點(diǎn)上。

在你奔跑途中的某一刻， 你會(huì)進(jìn)入這個(gè)節(jié)點(diǎn)，然后離開。

這就讓你經(jīng)過了兩條邊。

如果你再次進(jìn)入這個(gè)節(jié)點(diǎn)， 你也必須再離開一次，這就需要經(jīng)過另一對(duì)邊。

因此，你的路徑中的每一個(gè)點(diǎn) 都會(huì)有成對(duì)的邊。

每對(duì)中的一條邊是“入點(diǎn)”， 另一條邊則是“出點(diǎn)”。

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

There are just two exceptions: the start and end points, where you can exit without entering, or vice versa.?

If we look at the network formed by the serpent again, and number how many edges emerge from each node, a pattern jumps out that fits what we just saw.?

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

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

Interestingly enough, any connected network that has exactly 2 nodes with an odd number of edges will also contain an Eulerian path.?

The same is true if there are no nodes with an odd number of edges— in that case the path starts and ends in the same spot.

這也意味著從每個(gè)節(jié)點(diǎn) 出來的邊數(shù)必須是偶數(shù)。

只有兩個(gè)例外：起點(diǎn)和終點(diǎn)，你可以只離開不進(jìn)入， 也可以只進(jìn)入不離開。

如果我們?cè)倏纯从删奚咝纬傻木W(wǎng)，并數(shù)數(shù)從每個(gè)節(jié)點(diǎn)發(fā)出了多少條邊，一個(gè)與剛剛所見 相符的圖案便躍然而出。

除了兩個(gè)節(jié)點(diǎn)，其它每個(gè)節(jié)點(diǎn) 所連接的邊數(shù)都是偶數(shù)，這兩個(gè)例外中的一個(gè)肯定是起點(diǎn)， 另一個(gè)肯定是終點(diǎn)。

有意思的是，任何一個(gè)連通圖 如果恰好有兩個(gè)節(jié)點(diǎn)具有奇數(shù)條邊，那么這個(gè)連通圖肯定可以被一筆畫。

如果圖中沒有節(jié)點(diǎn)連接了奇數(shù)條邊， 這個(gè)圖同樣能被一筆畫——這種情況下，歐拉路徑 將在同一個(gè)點(diǎn)開始并結(jié)束。

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

We can begin by taking care of this edge here.?

Now we can zig-zag back and forth across the whole snake until we reach the end.?

And that's just one solution— it helps to be systematic, but you’re likely to happen upon many others once you know where to begin and end your run.?

You hold your hammer high at the opportune moment, and Odin sends the world-saving surge of lightning at you.?

Then you run like you’ve never run before.

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

And if something like that were out there, slouching its way towards you… well, that would be a story for another day.

知道這些之后，讓我們回到完整的圖。

我們可以先途經(jīng)這條邊，

然后就可以按 “之” 字形 來回繞完整條蛇，直到抵達(dá)終點(diǎn)。

這只是一種解法—— 保持條理性會(huì)讓一筆畫更容易，但只要知道了路徑的起點(diǎn)和終點(diǎn)，你或許能發(fā)現(xiàn)許多條可行的路徑。

你抓準(zhǔn)時(shí)機(jī)，將錘子高高舉起，奧丁便將拯救世界的 一道閃電朝你擲來。

然后你就拼了老命地撒腿狂奔，如果你能成功，想必再無他物 能阻止北歐眾神的威勢(shì)。

而假如還有像那樣的家伙 慢悠悠地拖著步子朝你走來……嗯，那就是后話了。