For the introductory problem:
I have heard of the controversy surrounding 45 000 000 000. I want you to know I do not favor the extremists who believe there is an integer larger than it.
I don't know about you but the problem before number 2, n^2 + 9 + 9 is amazing. That's a great toaster too,
I got a different answer to problem 3 but sorry that 8 pence answer totally beat me.
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.