FunFact

ProfessorSu's Fabulous Fun Facts! Find them at http://www.math.hmc.edu/funfacts/

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From an AnalExam:

Remove all numbers from the harmonic series whose denominators contain the digit 0 in their decimal representations. The resulting series converges to a number less than 90.

I believe AndrewSchoonmaker found a cute proof of this.

Unfortunately, said cute proof (a) requires assuming that the series converges and (b) often confuses people. Oh well.

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Every polyhedron of genus zero has at least one face with strictly fewer than six edges.

Hint: Think GraphTheory?.