[Math] the maximum number of pieces that a pizza can be cut into by 7 knife cuts? (NBHM 2005)

combinatorial-geometrydiscrete mathematicsgeometryreference-request

I am seeing this question very first time and do not know any formal way to solve it. Which part of mathematics it is related to?

What is the maximum number of pieces that a pizza can be cut into by 7 knife cuts?

A pizza is usually round shaped. So I was cutting a circle into pieces by seven straight lines. Minimum number is eight. But no maximum I am getting.

It is better to add complete answer with references. Thank you for your help.

Best Answer

This is a known problem: it is appropriately called the Circle Cutting Problem.

I suggest to you to read the linked page --- it is quite informative. However, the important part is that with $n$ cuts, you can divide a circle into at most $f(n)$ parts, where:

$$f(n) = \frac12\left(n^2 + n + 2\right)$$

In your case, $f(7) = \frac12(49+7+2) = \frac12(58) = 29$.

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