  We consider the solutions of the Guderley problem, consisting of an imploding
strong shock wave in an ideal gas with a power law initial density profile. The
self-similar solutions, and specifically the similarity exponent which
determines the behavior of the accelerating shock, are studied in detail, for
cylindrical and spherical symmetries and for a wide range of the adiabatic
index and the spatial density exponent. We then demonstrate how the analytic
solutions can be reproduced in Lagrangian hydrodynamic codes, thus
demonstrating their usefulness as a code validation and verification test
problem.
