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RU-SPB 2010 Problem 95

  • Grade 9

There are 20102010 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 Ministry destroys 10 free roads. Can Business create cyclic route without self-intersections through exactly 1111 different cities?

Dataset text AI-MO AoPS. Quoted with source.

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