Pairing points with disjoint line segments.
Maximal rooks and bishops.
Godly magic squares.
General position in chess: No-three-in-line problem.
Guessing a natural polynomial.
Frodo's number.
$G/Z(G)$ cyclic implies $G$ is abelian.
Center of quarternion group.
The 5/8 theorem, and the most abelian non-abelian groups.
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