Star Player
A star can be considered to divide an area into several regions, most of which are triangles and a small number of which are a different polygon.
With this in mind, what is the sum of the coefficients of the general equation for the number of regions a star with a Schläfli symbol of divides an area into?
The answer is 4.
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1 solution
A { 5 / 2 } star (i.e. n = 2 ) divides an area into 6 regions, a { 7 / 2 } star (i.e. n = 3 ) divides an area into 8 regions, and a { 9 / 2 } star (i.e. n = 4 ) divides an area into 10 regions.
The general equation for this is 2 n + 2 , so the sum of the coefficients is hence 2 + 2 = 4 .