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BALTIC-WAY 2018 Problem 10

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The integers from 1 to nn are written, one on each of nn cards. The first player removes one card. Then the second player removes two cards with consecutive integers. After that the first player removes three cards with consecutive integers. Finally, the second player removes four cards with consecutive integers. What is the smallest value of nn for which the second player can ensure that he completes both his moves?

Dataset text NuminaMath olympiads. Quoted with source.

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