  Propagation of a blast wave due to strong explosion in the center of a
power-law-density ($\rho \propto r^{-\alpha}$) spherically symmetric atmosphere
is studied. For adiabatic index of 5/3, the solution was known to be
self-similar, (of type I) for $\alpha <3$, self-similar (of type II) for
$\alpha >3.26$, and unknown in between. We find a self-similar solution for
$3<\alpha <3.26$, and give a (tentative) numerical proof that this solution is
indeed an asymptotic of the strong explosion. This self-similar solution is
neither of type I (dimensional analysis does not work), nor of type II (the
index of the solution is known without solving an eigenvalue problem).
