  It is known that if $(A,B)$ is a Leonard pair, then the linear
transformations $A$, $B$ satisfy the Askey-Wilson relations A^2 B - b A B A + B
A^2 - g (A B+B A) - r B = h A^2 + w A + e I,
  B^2 A - b B A B + A B^2 - h (A B+B A) - s A = g B^2 + w B + f I, for some
scalars $b,g,h,r,s,w,e,f$. The problem of this paper is the following: given a
pair of Askey-Wilson relations as above, how many Leonard pairs are there that
satisfy those relations? It turns out that the answer is 5 in general. We give
the generic number of Leonard pairs for each Askey-Wilson type of Askey-Wilson
relations.
