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RU-SPB 2012 Problem 117

  • Grade 11

Some cities of Russia are connected with some cities of Ukraine with international airlines. The Interstate Council for the Promotion of Migration intends to introduce a one-way traffic on each airline so that, by taking off from the city, it could no longer be returned in this city (using other one-way airlines). Prove that the number of ways to do this is not divided by 33 .

Dataset text AI-MO AoPS. Quoted with source.

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