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RU-SPB 2010 Problem 113

  • Grade 11

There are 20092009 cities in country, and every two are connected by road. Businessman and Road Ministry play next game. Every morning Businessman buys one road and every evening Minisrty destroys 10 free roads. Can Business create cyclic route without self-intersections through exactly 7575 different cities?

Dataset text AI-MO AoPS. Quoted with source.

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