TITLE: How to Slice the Cheese
QUESTION [8 upvotes]: I encountered a problem recently stated as below:
How many pieces of cheese we can obtain from a single thick piece by making five straight slices? (we can't move the cheese when slicing) If we want to maximize the number of pieces which is denoted by $P(n)$, is there any recurrence relation for $P(n)$, where $n$ is the number of slices?
Any hints will be highly appreciated.

REPLY [2 votes]: This is the lazy caterer's sequence. As others have mentioned, arbitrary dimensional analogues are called hyperplane arrangements.