  We consider the problem of resolving all pairwise interactions of shock
waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal
polytropic gas. Resolving an interaction means here to determine the types of
the three outgoing (backward, contact, and forward) waves in the Riemann
problem defined by the extreme left and right states of the two incoming waves,
together with possible vacuum formation. This problem has been considered by
several authors and turns out to be surprisingly involved. For each type of
interaction (head-on, involving a contact, or overtaking) the outcome depends
on the strengths of the incoming waves. In the case of overtaking waves the
type of the reflected wave also depends on the value of the adiabatic constant.
Our analysis provides a complete breakdown and gives the exact outcome of each
interaction.
