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Determine whether or nor there exist two disjoint infinite sets

A

and

B

of points in the plane satisfying the following conditions: a.) No three points in

A \cup B

are collinear, and the distance between any two points in

A \cup B

is at least 1. b.) There is a point of

A

in any triangle whose vertices are in

B,

and there is a point of

B

in any triangle whose vertices are in

A.

Problem Statement