Seven Bridges and Eight Bridges

A large blue and green rectangular exhibit.

Nodes and edges.

How it works

Each map shows a river flowing through a town, with two islands in the middle of the river. Starting from any point on a map, use the rope to mark out a continuous route that crosses every bridge only once.

Things to try or ask around the exhibit

Can you always find a route that crosses every bridge only once?

Background

This classic puzzle was developed in the 1700s by Swiss mathematician Leonhard Euler, who was inspired by the town layout of Königsberg and its seven bridges.

With the eight bridge puzzle, you can take a path that crosses each bridge only once. With seven bridges, you either have to miss a bridge, or cross one bridge twice.

The trick is the number of 'nodes' (river banks and islands) and 'edges' (bridge lines) that can be overlaid onto a map. Euler showed that Königsberg had a four-node network. Each node was joined by an odd number of edges, so a continuous path using each edge only once is impossible. Euler then found that to take a continuous path around any network, you must have 0 or 2 nodes that have an odd number of edges.