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Back in high school, I came across the following contest problem:

**Question: **Let be a set of positive integers totaling 20. What is the maximum value of

It’s a fun problem, so don’t rush past the spoiler tags too fast. When you’re ready, I’ll spoil the solution to the question above, and discuss a “continuous” version of the question above. Namely, what happens when is allowed to include positive real numbers?

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