Question 4
Some of the vertices of a regular $120$-gon are labeled by $*$. What is the maximal possible number of vertices labeled with $*$ if the following condition must be satisfied?
There exists no isosceles triangle with the angle at the top vertex of $18^\circ$ formed by $*$-labeled vertices of the $120$-gon.
There exists no isosceles triangle with the angle at the top vertex of $18^\circ$ formed by $*$-labeled vertices of the $120$-gon.