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In a certain country, 100 roads lead out of each city, and one can travel along those roads from any city to any other. One road is closed for repairs. Prove that one can still get from any city to any other.

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    I assume “100 roads” means *exactly* 100 roads, not *at least* 100 roads. For in the latter case, I can think of a counterexample. (Two complete graphs of 101 nodes/cities each, joined by a single edge/road between two cities, one in each group.)2012-11-09
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    Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post.2012-11-09

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