how can he figure out sum of daughters age=14
Hint 2 about sum is not clear
sum all combinations whose product is 72
are unique except 14
means 14 comes twice
now in question it is said that prof X knows the no of building
hence he know sum and product of ages
hence we find the value of x ,y and z
but there are 2 combinations (2 set of possible answers)
6 6 2 and 8 3 2 so it got confused
then y tell that he has only one oldest daughter
hence x figure out it is 8,3,2
i hope this helps
if have any doubt feel free to ask
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