Arraryeldergox2

2022-06-25

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 $P\left(n\right)$, is there any recurrence relation for $P\left(n\right)$, where $n$ is the number of slices?

iceniessyoy

Expert

This is a special case of the problem of counting the number of regions ${\mathbb{R}}^{n}$ is divided into by $k$ hyperplanes in general position. The answer is
$\sum _{j=0}^{n}\left(\genfrac{}{}{0}{}{k}{j}\right).$

Zion Wheeler

Expert