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, ab, where a, b < 100, what is the maximum digital sum?
So, let’s do nested loops, both going 1 to 100. Inside the inner loop, calculate a^b (or i^j in this case). Then loop through the digits of that value, adding them up. Keep track of which is the largest value this produces.
Running time about 3 seconds in Python:
import time tStart = time.time() maxsum = 0 for i in range(100): for j in range(100): num = i ** j total = 0 for k in str(num): total += int(k) if total > maxsum: maxsum = total print(maxsum) print("time:" + str(time.time() - tStart))