TITLE: Sword, pizza and watermelon
QUESTION [7 upvotes]: Suppose that we have a sword and cut a pizza and watermelon. What is the maximum number of pieces of pizza or watermelon obtained after 10 cuts. Is there a general formula

REPLY [3 votes]: You can get 1024 of each by rearranging pieces between cuts to all be cut in half with the next cut.  In fact, this is exactly how I make my famous samurai-ninja-watermelon-pizza salad, though I recommend skinning the rind from the watermelon first.  
Note:  I've also found that you can get even more pieces of pizza if you fold it like a kid's paper snowflake between cuts, but I've never personally made it over 8,192 pieces with this method...