  Finding the so-called characteristic numbers of the complex projective plane
${\mathbb C}P^2$ is a classical problem of enumerative geometry posed by
Zeuthen more than a century ago. For a given $d$ and $g$ one has to find the
number of degree $d$ genus $g$ curves that pass through a certain generic
configuration of points and at the same time are tangent to a certain generic
configuration of lines. The total number of points and lines in these two
configurations is $3d-1+g$ so that the answer is a finite integer number.
  In this paper we translate this classical problem to the corresponding
enumerative problem of tropical geometry in the case when $g=0$. Namely, we
show that the tropical problem is well-posed and establish a special case of
the correspondence theorem that ensures that the corresponding tropical and
classical numbers coincide. Then we use the floor diagram calculus to reduce
the problem to pure combinatorics. As a consequence, we express genus 0
characteristic numbers of $\CC P^2$ in terms of open Hurwitz numbers.
