The EHEP problem, as originally published by Fickett and Rivard, is quite useful for code verification but has some limitations. One limitation is the choice of *u*_{p} allowed under this exact solution. This article and the exact solution code assume properties of *u*_{p} also assumed by Fickett and Rivard, specifically that the piston is moving slowly to the right, with velocity bounded as 0 < *u*_{p} < *u*_{CJ}. This is the case of an *unsupported* detonation wave contained by a slow-moving piston.^{7} If the piston has value *u*_{p} = *u*_{CJ}, then, the theory states that the flow transitions from *unsupported* to *supported*, the rarefaction zone behind the shock (Region I in Fig. 2) vanishes and the region of constant properties (Region III in Fig. 2) extends from the piston to the shock front (boundary B to boundary A in Fig. 2). The value of *u*_{CJ} under the assumption of instantaneous detonation with infinitesimal reaction zones, and polytropic EOS, is given in Eq. (2.19) of Ref. [6] as *u*_{CJ} = *D*/(*γ* + 1). In this problem *γ* = 3, thus, the value *u*_{p} = *D*/4 is where the flow transitions from *unsupported* to *supported*. If the piston exceeds this velocity, the flow is considered to be *overdriven*. Referring to Fig. 2, graphically the situation of the rarefaction region (Region I) disappearing occurs when boundary A and boundary C are coincident. Solving Eqs. (22) and (27) simultaneously yields *u*_{p} = *D*/4, identical to what is predicted from the theory above. Thus, the flow is unsupported when *u*_{p} < *D*/4, supported when *u*_{p} = *D*/4, and overdriven when *u*_{p} > *D*/4. In this article, only the forward-moving, unsupported case is considered (0 < *u*_{p} < *D*/4). Another limitation of this problem is that the HE EOS is limited to a polytropic gas formulation. The assumption of a polytropic gas with *γ* = 3 is fundamental to the derivation of the exact solution, and it is unclear whether the exact solution could be extended to other cases.