  L\'{a}szl\'{o} Fejes T\'{o}th and Alad\'{a}r Heppes proposed the following
generalization of the kissing number problem. Given a ball in $\mathbb{R}^d$,
consider a family of balls touching it, and another family of balls touching
the first family. Find the maximal possible number of balls in this
arrangement, provided that no two balls intersect by interiors, and all balls
are congruent. They showed that the answer for disks on the plane is $19$. They
also conjectured that if there are three families of disks instead of two, the
answer is $37$. In this paper we confirm this conjecture.
