The only critical assumptions are that they are aware of the details of what both of them have been given and that if they could have known the answer they woul

The only critical assumptions are that they are aware of the details of what both of them have been given and that if they could have known the answer they would say so (i.e. that they are being perfectly logical and not making a mistake). The fact that this eliminates potential solutions is a consequence of that and the problem as set out. The whole puzzle hinges the fact that one person not knowing the answer from the part they are given (and the knowledge that the other person does not know after each step) constrains (i.e. gives information on) the answer. (but it is correct that as stated you could not derive all pairs of numbers this way: the puzzle gives you a sequence for which the pair is knowable)