MathDB

Let the set

S = \{P_1, P_2, \cdots, P_{12}\}

consist of the twelve vertices of a regular

12

-gon. A subset

Q

S

is called communal if there is a circle such that all points of

Q

are inside the circle, and all points of

S

not in

Q

are outside of the circle. How many communal subsets are there? (Note that the empty set is a communal subset.)

Problem Statement