It looks like one has to have a list of amino acid formulae (or know some aspects of the entries pretty well) to solve this. One doesn't have to calculate values for all atom types, but can work from aspects that are constant and constrained for all AAs or for certain subgroups of AAs. The problem is to have two PPs that have viable formulae and two that that violate constraints for a normal natural PP. Probably best to look for the two which have violations, as the good ones could have a wide possible range of atom numbers. Easier to find the violators, I think.

Interesting the OP has a bit of reasoning that's in the right sort of direction, but fouls it up. (This is all based on a version of the page before any edits or answers have been made.)