Question

Seven Bridges of Königsberg

Answer 1

Is it possible to take a walk through each part of the town, and crossing each bridge only once?

Answer 2

@EvL this intrigues me, I can't think of any

Answer 3

Answer: It is \(\sf not\) possible.

This is an application of Euler's circuit theorem (Graph Theory). This one says that for every vertex, it must have an even degree (which makes sense with this problem because we need entrance and exit). So I labeled each part of the town as A,B, C, and D (shown above)

Answer 4

A,B,C,D represent the vertices and the lines connecting them are called the paths. For the Euler's circuit, we must cross each path only ONCE. Based from the graph, you can see that A,C, and D vertices have an odd degree and therefore, it is not possible to cross these part of the town once. Btw, degree is the number of paths connecting to the vertex.

P.S. not sure if it is safe to use "nodes" and "vertices" interchangeably .

Answer 5

everything is possible.:-=|

Answer 6

I started only looking at the picture first to figure out if there was a way with where to begin before I scrolled down and saw the explanation

this is intriguing...