Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
1634 = 14 + 64 + 34 + 44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44
As 1 = 14 is not a sum it is not included.
The sum of these numbers is 1634 + 8208 + 9474 = 19316.
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
They key part of this algorthim is find the limit of our brute force search. What number should we go up to check for this special property? Consider a 4 digit number. The maximum of digit fifth power is 236196 which has 6 digit. Hence, searching up to 4 digit number isn't enough. How about 5 digits? 5 * 9^5 is 295245 which still has 6 digit. 6 digits? 6 * 9^5 is 354294 which has 6 digits! So, we can search all the way to 6 digits, specifically, 354294.
Answer: 443839
Runtime: 2.9 seconds