Once I went to my old handout and encountered this problem :
There are n points which pairwise have distance at least 1. Prove that we can choose $n/7$ points of them that pairwise have distance at least $\sqrt3$.
I've attemped for a week and I've come across to $n/12$ points with drawing rings with ratio of 1 and $\sqrt3$ over every points, there must at most 12 points in every rings.
what is your Idea about this problem?