We are given a fixed point on the circle of radius
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
, and going from this point along the circumference in the positive direction on curved distances
![0, 1, 2, \ldots](/media/m/9/4/0/940e5efeb8870a45e3db6768e55f8d63.png)
from it we obtain points with abscisas
![n = 0, 1, 2, .\ldots](/media/m/9/0/4/904e6c258ec1b3d07479e56076dffb3f.png)
respectively. How many points among them should we take to ensure that some two of them are less than the distance
![\frac 15](/media/m/b/4/8/b48f01b61dc7313c83a44c8cc0513862.png)
apart ?
%V0
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 ?