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.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.