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The Seven Bridges of Königsberg

The Seven Bridges of Königsberg was a famous 18th-century puzzle based on the layout of the city of Königsberg (now Kaliningrad, Russia), which had seven bridges connecting various parts of the city across the Pregel River. The challenge was to devise a walk through the city that would cross each bridge exactly once without repeating any. In 1736, mathematician Leonhard Euler proved that such a walk is impossible, marking the beginning of graph theory. He simplified the problem by representing landmasses as points (nodes) and bridges as lines (edges), and discovered that a walk crossing each bridge once (an Eulerian path) is only possible if the graph has exactly zero or two nodes with an odd number of connecting edges. Since all four regions in Königsberg had an odd number of bridges, the walk was not possible. Euler's work on this problem laid the foundation for modern graph theory and topology.

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