Solve the Ragnarok Riddle: Can You Save Valhalla?

Ragnarok, the prophesied end of the world in Norse mythology, unfolds with gods, giants, and monsters locked in an epic battle. Just when the gods seem to have the upper hand, the monstrous serpent Jörmungandr emerges, swallowing Valhalla and coiling across the land, creating a single, continuous body with no discernible head or tail. Odin, on the brink of exhaustion, musters one final lightning strike. Armed with the mighty hammer Mjölnir, you are humanity's last hope. Can you and Odin together destroy the serpent and prevent the fall of Valhalla?

The Challenge: A Serpent's Maze

Your task is to run along Jörmungandr's immense body. At the opportune moment, you'll raise Mjölnir, and Odin will strike it with lightning, splitting the serpent open. However, the challenge doesn't end there. You must continue running along its body until every part is destroyed, without retracing your steps over already blasted sections. You are allowed to pass through points where the serpent intersects itself multiple times.

Failure means Jörmungandr regenerates, Odin's power is spent, and Valhalla is doomed. What path will you take to ensure the serpent's complete destruction?

Simplifying the Problem: Graph Theory to the Rescue

To solve this seemingly impossible riddle, we can simplify the problem by focusing on two key elements:

Intersections: Points where the serpent crosses itself.
Stretches of Snake: The paths between these intersections.

In the language of graph theory, these elements are known as nodes and edges, respectively. The edges represent the paths we must travel, while the nodes are the junctions where we make crucial decisions.

This simplification transforms the serpent into a graph, or network, a fundamental concept in mathematics. Our goal is to find an Eulerian path, a route that traces every edge exactly once.

The Key to the Path: Even and Odd Nodes

Consider a single node along your path. You'll enter it and then exit it, accounting for two edges. If you enter again, you must exit again, requiring another pair of edges. This means that, for most nodes, the number of edges connected to them must be even.

There are two exceptions: the start and end points of your journey. At the starting point, you exit without entering, and at the end point, you enter without exiting. These nodes can have an odd number of edges.

Looking at the serpent's network, we can count the number of edges emerging from each node. If the network is connected and has exactly two nodes with an odd number of edges, an Eulerian path exists. If there are no nodes with an odd number of edges, the path starts and ends at the same point.

Finding the Solution: A Step-by-Step Approach

Identify the Start and End Points: Locate the two nodes with an odd number of edges. These will be the beginning and end of your path.
Plan Your Route: Begin at the starting node and systematically traverse the edges, ensuring you cover each one exactly once. Zig-zagging back and forth can be an effective strategy.
Avoid Retracing: Be mindful not to run over any section of the serpent that has already been blasted.

With this knowledge, you can find a path to destroy Jörmungandr. Remember, being systematic is key, and there may be multiple solutions.

Victory and the Future

You hold Mjölnir high, and Odin unleashes the world-saving surge of lightning. You run with unparalleled speed, ensuring every segment of the serpent is obliterated. Valhalla is saved, and the might of the Norse gods prevails.

But what if something else were out there, something even more formidable? That, as they say, is a story for another day.

Can you solve the Ragnarok riddle and save Valhalla?