For problem B (at least in the list=set version I did) we can indeed prove uniqueness for the solution "19": As mentioned before, 20 is not a solution; now add "n" to every sum=20 and multiply every product by n, to see that 20+n also is not a solution. This rules out every integer >19, except that there are a few cases where n was already used in the proof 20 was not a solution, hence adding n is forbidden since "set," not "multiset," of numbers summing to 20. But, all those cases, as it happens, were already ruled out anyhow by the computation I originally did. QED. Somebody might also want to work out the list=multiset version of Pizzahut problem B... the answer(s) if any, must be either 0,1,2,... or 19. I'd also be interested to know what Dan Asimov concluded about problem C, his post was rather mysterious. My own investigation of C was likely flawed and/or incomplete in some manner; I think I had some valid thoughts, but they probably were more "a good start" than "the full answer."