**Problem 56:**

A googol (10^{100}) is a massive number: one followed by one-hundred zeros; 100^{100} is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, *a ^{b}*, where

*a, b*< 100, what is the maximum digital sum?

**Idea:**

I was wondering how long it was going to be until googol came up in a problem (although I was part expecting googolplex)

I didn’t see any easy way to do this, as it’s pretty straight forward, raise a to the power of b, for all possible combinations of a and b < 100, take the sum of the digits, and repeat until you reach 99^{99}, keeping track of the maximal sum.