#56 - Powerful digit sum

19 Jun 2017 in Project Euler on 5%

A googol $\left(10^{100}\right)$ 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?

---

Another straightforward problem. All we need to do is loop through all $a$ and $b$, compute $a^b$, and add the digits together.

# file: "problem056.py"
maxSum = 0
for a in range(1, 100):
    for b in range(1, 100):
        s = sum(int(x) for x in str(a ** b))
        if s > maxSum:
            maxSum = s

print(maxSum)

output of the above is,

Max digital sum at 99^95 with a sum of 972
0.2502726912502948 seconds.

Thus, $99^{95}$ has the maximum digital sum of 972.