IMO Shortlist 1968 problem 19


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2. travnja 2012.
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We are given a fixed point on the circle of radius 1, and going from this point along the circumference in the positive direction on curved distances 0, 1, 2, \ldots from it we obtain points with abscisas n = 0, 1, 2, .\ldots respectively. How many points among them should we take to ensure that some two of them are less than the distance \frac 15 apart ?
Izvor: Međunarodna matematička olimpijada, shortlist 1968