Is it possible to walk the seven bridges of Konigsburg so that you cross every bridge exactly twice, once in each direction? Why or why not?

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- December 11th 2009, 10:25 AMdynas7yVariation of Konigsburg Bridge Problem
Is it possible to walk the seven bridges of Konigsburg so that you cross every bridge exactly twice, once in each direction? Why or why not?

- December 11th 2009, 11:54 AMemakarov
We can consider a directed multigraph. A simple directed graph has the following criterion: A directed graph is Eulerian iff it is strongly connected and every vertex has equal in degree and out degree. The same is probably true for a multigraph.

In our case, the criterion is true, so I believe the answer to the original question is yes.

A remark: To maximize chances for a helpful reply, it may be a good idea to explain some notions that are not central to the problem. In this case, one may know about Eulerian graphs but not about Königsberg. - December 11th 2009, 05:01 PMdynas7y
Thank you, and yes I will explain concepts in more detail in future questions. Also, the answer to this question is yes and I was able to verify this with finding an actual path that satisfies the given conditions.