Did you deduce the building number just because he "still didn't know" and 14 was the only double? Isn't it possible he didn't know because of other reasons, rather than the available options. Maybe he just couldn't figure out all the options of factors of 72, maybe he couldn't literally see the building number :)

Maybe. But you have to take into account they are both MIT math grads. I guess here MIT math grads stands for ideally perfect maths (are they? ;-) and so we can presume he is able to solve the system with the two Diophantine equation.

The other objection - that he couldn't see the building number - is more serious. I guess any MIT math grad - even if he has myopia and is lazy - has an excess of Perl hubris (As defined by Larry_Wall excessive pride, the sort of thing Zeus zaps you for ...) so that he will do whatever to show off his skills, including to cross the road to look at the number :-).