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RU-SPB 2018 Problem 97

  • Grade 9

In 10×1010\times 10 square we choose nn cells. In every chosen cell we draw one arrow from the angle to opposite angle. It is known, that for any two arrows, or the end of one of them coincides with the beginning of the other, or the distance between their ends is at least 2. What is the maximum possible value of nn ?

Dataset text AI-MO AoPS. Quoted with source.

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