Powerful digit sum¶

A googol (10¹⁰⁰) is a massive number: one followed by one-hundred zeros; 100¹⁰⁰ 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¶

Naive solution, as instructed.

import sys, os; sys.path.append(os.path.abspath('..'))
from timer import timethis

def get_digit_sum(n):
    s = 0
    while n:
        s += n % 10
        n //= 10
    return s

get_digit_sum(123)

6

@timethis
def solve():
    m = 0
    for a in range(100):
        for b in range(100):
            n = pow(a, b)
            m = max(m, get_digit_sum(n))
    return m

solve()

Run for 0.312 seconds

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