Trusted answers to developer questions

Kainat Asif

- A googol ($10^{100}$) is a massive number, i.e., one followed by one hundred zeros.
- $100^{100}$ ($10^{200}$) is almost unimaginably large, i.e., 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?*

```
Maximum digital sum = 972
```

Let’s look at the code snippet below. It gives a solution for how to calculate the powerful digital sum of a, b < 100.

a = 100 b = 100 maxSum = 0 for i in range(a): for j in range(b): temp = i**j #i**j = i^j temp = map(int, str(temp)) #mapping int to string as it is less costly to parse strings than dealing with big integers sumList = list(temp) #making a list of numbers tempSum = sum(sumList); #calculating sum of digits if(tempSum > maxSum): maxSum = tempSum #finding max sum print "Maximum digital sum = ", maxSum

The nested loop calculates the exponent $i^{j}$, where 0<i<100 and 0<j<100. The sum of the digits of the exponent is calculated in *line 10* and the maximum digit sum is stored in `maxSum`

in *line 12*. This is the *powerful digital sum* $a^{b}$ for a<100 and b<100.

RELATED TAGS

project euler

CONTRIBUTOR

Kainat Asif

Copyright ©2022 Educative, Inc. All rights reserved

RELATED COURSES

View all Courses

Keep Exploring

Related Courses