  This is a first step in counting the number of multiple solutions in certain
glassy random matrix models introduced in refs. \cite{d02}. We are able to do
this by reducing the problem of counting the multiple solutions to that of a
moment problem. More precisely we count the number of different moments when we
introduce an asymmetry (tapping) in the random matrix model and then take it to
vanish. It is shown here that the number of moments grows exponentially with
respect to N the size of the matrix. As these models map onto models of
structural glasses in the high temperature phase (liquid) this may have
interesting implications for the supercooled liquid phase in these spin glass
models. Further it is shown that the nature of the asymmetry (tapping) is
crutial in finding the multiple solutions. This also clarifies some of the
puzzles we raised in ref. \cite{bd99}.
