## Common Problems

This is pretty cool. What is the value of the following expression?

4 + π5)1/6

This reminds me of a series of problems that I call Maximum Mileage:

1. What is the maximum possible product of two positive integers whose sum is 100?
2. What is the maximum possible product of two prime numbers whose sum is 100?
3. A set of positive integers has a sum of 100. What is the maximum possible product of the numbers in this set?
4. A set of positive numbers has a sum of 100. What is the maximum possible product of the numbers in this set?

Bonus Question: Why does the expression at the beginning of this post remind me of that series of problems?

The following sentence might be a hint:

It is fortuitous that both conundrums incur a commonality of solution.

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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