The Seven Bridges of Königsberg/Section 20

by Leonhard Euler

Thus for any configuration that may arise the easiest way of determining whether a single crossing of all the bridges is possible is to apply the following rules:

• If there are more than two regions which are approached by an odd number of bridges, no route satisfying the required conditions can be found.
• If, however, there are only two regions with an odd number of approach bridges the required journey can be completed provided it originates in one of the regions.
• If, finally, there is no region with an odd number of approach bridges, the required journey can be effected, no matter where it begins.

These rules solve completely the problem initially proposed.