## Archive for November 30, 2013

### Common Problems

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

(π^{4} + π^{5})^{1/6}

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

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