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IMO LongList 1967, Soviet Union 6

Source: IMO LongList 1967, Soviet Union 6

December 16, 2004
combinatoricsgeometrycountingcircleIMO ShortlistIMO Longlist

Problem Statement

On the circle with center 0 and radius 1 the point A0A_0 is fixed and points A1,A2,…,A999,A1000A_1, A_2, \ldots, A_{999}, A_{1000} are distributed in such a way that the angle ∠A00Ak=k\angle A_00A_k = k (in radians). Cut the circle at points A0,A1,…,A1000.A_0, A_1, \ldots, A_{1000}. How many arcs with different lengths are obtained. ?
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