I solved all three problems in under a half-hour by writing quick-and-dirty Java programs to do it. The standard libraries provide almost everything I needed; the only thing I used other than that was Maple to factor the number. I'm pretty sure mucking around with CPAN libs such would have taken me longer. Granted, my solutions were brute-force and not very elegant, but for simple problems like these with small inputs I can write code to solve it faster than finding the answer elsewhere.
