Euler realised that the reason for there being no solution depends on the degree of the nodes (in this case the land masses). The degree of a node is the number of edges (bridges) connected to it. Every node in this puzzle has an odd degree (three or five). In order for a solution to exist there must only be only 2 nodes with odd degrees and they must be the starting and ending nodes. For example in the Konigsberg Bridge problem once you arrive to a land mass you have a bridge to leave, but when you arrive again on another bridge there is no bridge left you can cross to get out.

Euler noticed that every landmass has an odd number of bridges connected to it. If you want to traverse all the bridges, then you would eventually be stuck

When we disceminate the problem, we find it is simply finding an Euler path in the graph representing Konisberg. From graph theory we know that an Euler path exists iff every node or EXACTLY two nodes have even degree. \define degree
Thus when we look at Konisberg, we see every node has odd degree and thus it is impossible to find an Euler path!

Mathematically, the problem can be translated to graph theory by viewing the land masses as nodes and the bridges as edges of a graph. Euler proved the general result that for there to be a path that visits each edge exactly once either all, or all but two vertices must have an even number of vertices connected to them (such a path is now called an \emph{Eulerian path}). As this is not the case for the landmasses and bridges of K\"{onigsberg}, there cannot be such a path.