So after reading the solutions to assignment 1 (I was bored and decided to see how they looked) I've realized that my solution style is completely different to the sample. So as a sample on other methods of presenting proofs: I link my solution! Which I think looks beautiful of course :)

https://docs.google.com/open?id=0BwY_GV-lFUUzamJoSnlDYXNYMmM

As a note I did not receive full marks. The error was in question 1 -_-; If you look carefully at question 1 I did not actually use Complete Induction, I used Mathematical Induction :( And it wasn't explained really well due to the lack of words. Basically, the idea was a full ternary tree of height n satisfies P(n) and since all ternary trees of height n have less than or equal number of nodes to the full ternary tree, they satisfy P(n) as well. I should of put
F(n) = F(n-1) + 3*l
N(n) <= F(n)
before
N(n) <= F(n-1) + 3*l
to clarify it a little more.. Oh wells.

My solution to the last question is also really different to that of the sample, so I will explain it in a number of posts this week; Yay!