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You could probably perform some sort of math personality test by asking which proof the respondent likes best! I was particularly charmed by #5 (construct a volume of revolution, then slice it two ways).

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For me it's #4. I think this was a trick Feynman used a lot. I always like seeing intimidating problems solved simply with an uncommon tool.

I also liked 4. I remember this being a trick question on a calc exam right after we learned differentiation under the integral.

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