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RU-SPB 2015 Problem 96

    There are 10201510^{2015} planets in an Intergalactic empire. Every two planets are connected by a two-way space line served by one of 20152015 travel companies. The Emperor would like to close kk of these companies such that it is still possible to reach any planet from any other planet. Find the maximum value of kk for which this is always possible.

    (D. Karpov)

    Dataset text AI-MO AoPS. Quoted with source.

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