Here we can discuss and explore the "Slicing the Cake" problem.

Take a circle and put $n$ points on its circumference. Join them all with straight lines. How many pieces can you get? The points don't need to be equally spaced - what's the largest number of pieces?

Points 1 2 3 4 5 6 7 8 9 10 ...
Pieces 1 2 4 8 16 . . . . 256 ...

This is one of the many Enrichment tasks on this site.

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