Find c and smallest n that satisfy the constraints

binomdist(c,n,p1,true)=1-alpha
binomdist(c,n,p2,true)<=beta

For the case p1=.001, p2=.002, alpha=.05, beta=.05, solver found the
solution

c=23, n=16288

Solver could not find the solution for the case p1=.01, p2=.05,
alpha=.05, beta=.10.

The solution, found by trial and error, is c=3, n=110.

Is this an idiosyncrasy of solver, or am I doing something wrong?

John Adams