Problem:
A set of points in the -plane is symmetric about the origin, both coordinate axes, and the line . If is in , what is the smallest number of points in
Answer Choices:
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Solution:
The set is symmetric about the line and contains , so it must also contain . Also is symmetric about the -axis, so it must contain and . Finally, since is symmetric about the -axis, it must contain , and . Since the resulting set of points is symmetric about both coordinate axes, it is also symmetric about the origin.
The problems on this page are the property of the MAA's American Mathematics Competitions