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 ...

• What is the formula?
• Warning - it's not what you think!
• How can you tell?

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

CategoryMaths