The Königsberg Problem

Each Graph Theory class would mention the Königsberg problem once. The problem is simple but the solution isn’t. Basically, there was a city in Prussia (old Germany) called Königsberg (now known as Kaliningrad and it is now in Russia) with 7 bridges over a river. The problem statement was to find a path that could cross each bridge just once in such a way that one could return back to the point where one started.

The solution is anti-climactic though. Mathematician Euler solved this by proving that there is no solution possible. I won’t go into his mathematical proof but anyone can try as hard as they want but the problem in its original form cannot be solved as such. So, the solution is that there is no solution.

I guess there is a lesson in this. Some problems cannot be solved. We can try as hard as possible, look at things from any direction possible, try to apply as much brainpower as possible, but sometimes they cannot be simply solved. It is better to move on to something else if changing the problem statement itself isn’t possible. Not everything is a compromise. Somethings are unsolvable.

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