as mentioned in the solution ...
3 6 ... NO - it is impossible to create any pair of numbers from the given sum, where there would be at least one sum (created from their product) bigger than 14
if 3 and 6 then they would think the following ...
A teacher says: I'm thinking of two natural numbers bigger than 1. Try to guess what they are.
The first student knows their product (18) and the other one knows their sum (9).
First: I do not know the sum.
Second: I knew that. (pairs of numbers that have sum of 9 can have various products) The sum is less than 14. (here is the problem, I thought that there would be some other combination for which sum would be bigger than 14 and thus I would help you by eliminating that combination ... but for sum of 9 there is no such combination ... whereas for sum 11 there is - 7 and 4 - which would make the product of 28 - that could be 14 and 2 as well - so 16 is bigger than 14 ... the same for 8 and 3, 5 and 6)
First: I knew that. (there is no way to have sum of 2 numbers 14 or more, when their product is 18 ... but you must have thought that I do not know it - and that's the problem - you did not know that) However, now I know the numbers.
Second: And so do I.
What were the numbers?