We present an algorithm for counting the number of integer solutions to selected free variables of a Presburger formula. We
represent the Presburger formula as a deterministic finite automaton (DFA) whose accepting paths encode the standard binary
representations of satisfying free variable values. We count the number of accepting paths in such a DFA to obtain the number
of solutions without enumerating the actual solutions. We demonstrate our algorithm on a suite of eight problems to show that
it is universal, robust, fast, and scalable.