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Discrete Mathematics Level 5

A pizza in the shape of a regular \(n\)-gon is sliced in an unusual way:

  1. Each cut is a straight line segment
  2. No cuts intersect inside the pizza
  3. Cuts are only made from one vertex to a non-adjacent vertex
  4. Only \(n - 3\) cuts are made

How many ways can a 16-gon pizza be sliced?

Details and Assumptions

The pizza has non-uniform topping placement; rotated or flipped solutions are counted separately.

For example, a pentagon pizza can be sliced 5 ways, as depicted in the image.

The pieces don't necessarily need to be of equal area.

This is not an original problem.


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