Problem 56

Problem 56

07 November 2003

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?

def fun56():
    result = [0,0,0]
    for i in range(2, 100):
        for j in range(1,100):
            t = i**j
            t = reduce(add, map(int, str(t)))
            if t > result[0]:
                result = [t,i,j]
    return result

answer is 972, 99**95
time:1.125