In 1736 Euler proved that nobody could walk through Königsberg crossing each of its seven bridges exactly once. Every patch of land touched an odd number of bridges, and a walk has only two ends to spend its odd counts on. That proof is usually named as the start of graph theory. Then the city changed underneath it. Two bridges were lost to bombing in the Second World War, two more were cleared for a Soviet highway, and today, in Kaliningrad, there are five bridges on the old sites. With five, the walk Euler ruled out can be done, as long as you start on one island and finish on the other. Nobody solved the puzzle. They just took away enough of the city that it stopped being one.