  We solve generalizations of Hubbard's twisted rabbit problem for analogues of
the rabbit polynomial of degree $d\geq 2$. The twisted rabbit problem asks:
when a certain quadratic polynomial, called the Douady Rabbit polynomial, is
twisted by a cyclic subgroup of a mapping class group, to which polynomial is
the resulting map equivalent (as a function of the power of the generator)? The
solution to the original quadratic twisted rabbit problem, given by
Bartholdi--Nekrashevych, depended on the 4-adic expansion of the power of the
mapping class by which we twist. In this paper, we provide a solution that
depends on the $d^2$-adic expansion of the power of the mapping class element
by which we twist.
