You and two friends decided to order a large circular pizza to split between each other. Unfortunately at the moment you didn't have enough to pay your entire third of the bill. Your friends decide that they will cover the remainder of your bill but for a cost! Instead of just giving you less pizza, they will give you a challenge to earn as much as you can. This is the challenge:
The pizza will be set up on a large cutting board.
You will be given 1 pizza cutter and are allowed to make 3 cuts in total.
Each cut must go from one end of the board to the other. (i.e no 'half cuts' or stopping in the middle of the pizza)
You are allowed to set it up how you please before and after each cut.
When you are finished cutting the pizza, you're friends will pick all their slices first, and they will take the higher number if distribution isn't 'fair'
(i.e if there are 4 slices, [Friend 1] will take 2, [Friend 2] will take 1 and then [You] will take 1)
(5 slices: [Friend 1] takes 2 then [Friend 2] takes 2 then You take 1)
**You must not cut it into the standard 6th's as done by normal pizza places (60° from each cut)
(Sorry for the last rule but your hungry friends have became cranky)
Your friends are really hungry and will always try to take as much pizza as possible.
What is the maximum amount of pizza you can get if you follow these rules?
If you are still restricted to 3 cuts, but you are allowed to distribute the pizza however you please (as long as your friends always have equal or more than you) how can you cut and distribute the pizza such that you all get even portions (The max as possible for you)?