IMO Shortlist 1967 problem 6
Dodao/la:
arhiva2. travnja 2012. On the circle with center 0 and radius 1 the point
![A_0](/media/m/2/f/f/2ff029e43a310c5b6d8137a3edb7609c.png)
is fixed and points
![A_1, A_2, \ldots, A_{999}, A_{1000}](/media/m/f/1/6/f1670f27c1738a6fd57bd57a25f9ae87.png)
are distributed in such a way that the angle
![\angle A_00A_k = k](/media/m/d/4/8/d487c2027c732c200460275389196235.png)
(in radians). Cut the circle at points
![A_0, A_1, \ldots, A_{1000}.](/media/m/b/1/4/b147fd1b1dc0c2751d93fba419ab82c1.png)
How many arcs with different lengths are obtained. ?
%V0
On the circle with center 0 and radius 1 the point $A_0$ is fixed and points $A_1, A_2, \ldots, A_{999}, A_{1000}$ are distributed in such a way that the angle $\angle A_00A_k = k$ (in radians). Cut the circle at points $A_0, A_1, \ldots, A_{1000}.$ How many arcs with different lengths are obtained. ?
Izvor: Međunarodna matematička olimpijada, shortlist 1967