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 ) .