AbstractThe Riemann problem for the unsteady one‐dimensional Euler equations together with the constant‐covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial‐boundary value problem for the Euler equations. The iterative procedure to findp*, the pressure between the acoustic waves, involves a single algebraic (non‐linear) equation, all other quantities follow directly throughout thex–tplane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choi