Find all integers $n > 1$ for which there is a set $B$ of $n$ points in the plane such that for any $A \in B$ there are three points $X,Y,Z \in B$ with $AX = AY = AZ = 1$.
Source: Romania IMO TST 1993 2.3
Tags: combinatorics, combinatorial geometry
Find all integers $n > 1$ for which there is a set $B$ of $n$ points in the plane such that for any $A \in B$ there are three points $X,Y,Z \in B$ with $AX = AY = AZ = 1$.