**EMT 725**

**Philippa M. Rhodes**

**What is the maximum number of pieces into which a pie can be sliced
with n straight cuts?**

Try some examples, make a chart, try to derive a formula.

The objective when trying to make the straight cuts to obtain the most possible pieces is to cross the previous cuts. For example, when I make cut # 3, I try to cross cuts #1 and #2.

Since we have let n = the number of cuts, we can see that the number
of pieces is the **sum
of the first n integers** plus 1. Therefore, a formula that will allow
us to determine the maximum number of pieces into which a pie can be sliced
with n cuts is: