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This at least was the solution offered by Sam Loyd, popular nineteenth century American puzzle columnist, who researched the number of bridges and found eight. But Euler, living 500 miles away in St. Petersburg, thought there were seven, and came to a different conclusion. First he scorned the problem as unworthy of a mathematician, then he looked at it, decided the problem could not be solved, and proceeded to create an analysis so insightful that it became the basis for the graph theory so crucial to modern search engines. |
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Euler focused not on the bridges ( } but on the turning points ( ) and saw that to enter and exit by unique routes there would have to be an even number of paths, except where you start and finish. With 7 bridges this was not possible, but with an 8th bridge -- real or imagined -- the puzzle could be solved. |
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| Grab your trench coat and let's go to Venice. A spy you are tracking has left behind a map of the city showing the canals and bridges. You know from following him for weeks that he has a set pattern for getting from his flat to the Cafe di Spia where he meets his handler. Partly to lose you, and partly because he is a little obsessive compulsive, he always crosses every bridge once and only once on his way. He never crosses the river to the north or south, and just moves from sector to sector. Since you have just been reading up on your Euler, you know without even tracing his path which two sectors he travels between, but you trace it anyway because, well, you are a little compulsive yourself, right? |
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