The Königsberg Bridges Revisited

In the old city of Königsberg, a river split the land into separate islands connected by seven bridges. The puzzle sounded harmless: Could someone walk through the city crossing each bridge exactly once? People tried repeatedly. Again and again they failed. Eventually the problem reached the Swiss mathematician Leonhard Euler. Euler did something revolutionary. He ignored the physical appearance of the city almost completely. The exact lengths of the bridges did not matter. The shape of the river did not matter. The architecture did not matter. Only the connections mattered. Euler reduced the city in