2. Consider all factorizations of 2450 into integers a, b, c.  (Since
these three variables represent ages, all factors above 98 should
be excluded!)  The remaining triples (a,b,c) sum to distinct values
_except_ 50+7+7 = 49+10+5 = 64.  Since the assistant did not have
enough information at this point, one of these two triples must be the
correct answer; in particular, the secretary's age is 64/2 = 32.
If the professor is 49 years old or younger, her assertion about
being older than all others at dinner cannot be true; if she is 51
or older, that information would not help the assistant.  Hence,
the professor is 50, and her dinner guests had ages 49, 10, 5.