 Seven Bridges of Königsberg

Model the four land regions by vertices $A,B,C,D$ and the seven bridges by distinct edges: two $AB$, two $AC$, and one each of $AD,BD,CD$. Their vertex degrees are $(5,3,3,3)$. Leonhard Euler's paper records these connections in §6 and the obstruction in §9; §20 states the zero-or-two odd-region rule. Four odd vertex degrees exclude an Eulerian trail, even if returning to the starting vertex is optional.^[ref]