MathDB

Let

P

be a cyclic polygon with circumcenter

O

that does not lie on any diagonal, and let

S

be the set of points on 2D plane containing

P

and

O

.
The

<span class='latex-italic'>Matcha Sweep Game</span>

is a game between two players

A

and

B

, with

A

going first, such that each choosing a nonempty subset

T

of points in

S

that has not been previously chosen, and such that if

T

has at least

3

vertices then

T

forms a convex polygon. The game ends with all points have been chosen, with the player picking the last point wins.
For which polygons

P

can

A

guarantee a win?
Proposed by Anzo Teh Zhao Yang

Problem Statement