Euler hatte dann auch allgemein untersucht, welche Bedingungen ein Stadtplan erfüllen muß, damit es einen solchen Spaziergang gibt: Die einzige Bedingung ist, daß jeder Teil von einer geraden Anzahl von Brücken zu erreichen ist.

Crowds each ev'ning surged towards the river,
People walked bemused across the bridges,
Pondering a simple sounding challenge
Which defeated them and left them puzzled.

Here's the problem; see if you can solve it!
Try it out at home on scraps of paper,
Starting out and ending at the same spot,
You must cross each bridge just once each evening.

Eulerian graphs all have this restriction:
THE DEGREE OF ANY POINT IS EVEN.
That's the oldest graph result
That mankind has ever known.

All the folk in Konisberg were frantic!
All their efforts ended up in failure!
Happily, a learned mathematician
Had his house right there within the city.

Euler's mind was equal to the problem
"Ah", he said, "You're bound to be disheartened,
Crossing each bridge only once per outing
Can't be done, I truly do assure you.

Laws of Nature never can be altered,
We can't change them, even if we wish to.
Nor can flooded rivers or great bridges
Interfere with scientific progress.

War brought strife and ruin to the Pregel,
Bombs destroyed those seven splendid bridges.
Euler's name and fame will, notwithstanding,
Be recalled with Konigsberg's for ever.