Project Euler

Problem

This problem comes from Project Euler 30

Problem

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

$1634 = 1^4 + 6^4 + 3^4 + 4^4\\ 8208 = 8^4 + 2^4 + 0^4 + 8^4\\ 9474 = 9^4 + 4^4 + 7^4 + 4^4$

As $1 = 1^4$ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19 316. Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

Solution

This problem is interesting because it doesn’t mention a scope. How do we know when to stop searching for numbers that can be written as the sum of the fourth/fifth power of their digits? I don’t know myself, but I made some assumptions.

In the problem there four digits that can be raised to the fourth power. So the range for this problem would be $4 \times 9^4 = 9^4 + 9^4 + 9^4 + 9^4$ . So by that, our maximum search would be $5 \times 9^5$ .

With that assumption made, we’ll go through each number as the problem states and find the numbers that are sums of their digits raised to the fifth power.

Code

# Project Euler: Problem 30
# Digit Fifth Powers

n = 5
search_range = n*(9**n)
sum_digits = 0

for number in range(2, search_range):
    num = [int(i) for i in str(number)]
    result = sum(map(lambda i: i**n, num))

    if result == number:
        sum_digits += number

    # This block is optional
    # For no apparent reason it allows the code
    # to execute on my computer ~200ms faster
    if result > search_range:
        break

print(sum_digits)

Also note the mysterious, “useless” code. Yep, without it my code takes ~770ms to execute, and with it it takes ~530ms to execute. No idea why.