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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 serpentrmungandr 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.

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

  • 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 splitrmungandr 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.

  • If you leave any portion un-zapped, Jörmungandr 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

  • 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.

  • 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.

  • 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.

  • 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 solutionit 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.

Ragnarok. The fabled end of the world,


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B1 中級

你能解開魔戒之謎嗎?- Dan Finkel (Can you solve the Ragnarok riddle? - Dan Finkel)

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    林宜悉 發佈於 2021 年 01 月 14 日