The Bridges of Königsberg

There is a city that no longer exists under its old name, and in that city there was a river, and in the river there were two islands, and connecting the islands and the riverbanks were seven bridges. The people of Königsberg had a game. On a Sunday walk, could you cross every bridge exactly once? You could start anywhere, end anywhere. You could take any route. The only rule: each bridge gets one crossing. No repeats, no skips. Everyone tried. No one succeeded. But no one could prove it was impossible, either. It sat there for years — a parlor puzzle, a Sunday afternoon frustration, the kind of problem that feels like it should yield to persistence. Your instinct is probably the same instinct the townspeople had. You want to try routes. Start on the north bank, cross to the first island, go south, loop around. You want to draw lines on a map and trace paths with your finger. That is what everyone did.