What is the maximum number of pieces of pizza possible when it is cut with 5 straight line cuts (the lines don't go through the center of the pizza.)? What is the maximum number of pieces of pizza possible when cut with 5 straight lines, none of which pass through the center of the pizza?
 A: I get $16$ pieces, based on a star:

Each added line cuts every prior line (and circumference)... a greedy algorithm.  The fact that each region is convex means that you cannot do better than that.
If you analyze it by counting the number of pieces added by each cut, you find that the number of pieces, $p$, as a function of number of cuts, $n$, is:
$$p(n) = 1 + \frac{n + n^2}{2}$$
$$
\begin{array}{c|ccccccccccc}
 n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
 p & 1 & 2 & 4 & 7 & 11 & 16 & 22 & 29 & 37 & 46 & 56 \\
\end{array}
$$

Note:  the problem constraint that lines not pass through the center of the pizza is irrelevant.
A: I think the logic is the following:
 Every next line should cross all the previous ones separately.
 If so, then the answer is 16.
Let the number of lines be $L$ and the maximum number of sections be $S$. 
 I suggest the following pattern(which is really interesting):
$$L \quad S$$
$$______$$
$$1 \quad 2$$
$$2 \quad  4$$
$$3 \quad 7$$
$$4 \quad 11$$
$$5 \quad 16$$
$$...$$
 Notice that $ S_{n+1} = S_n +L_{n+1} .$
$$\  $$ I know that this doesn't provide a proof, but it is interesting.
