# Euler Problem 30¶

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 $1634 + 8208 + 9474 = 19316$.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

This is an eays brute force. We look up the fifth powers.

In [7]:

    fifth_power_lookup = {str(i): i**5 for i in range(0,10)}

    def is_number_sum_of_fiths_powers_of_digits(n):
        return n == sum([fifth_power_lookup[d] for d in str(n)])

    s = sum([i for i in range(1, 1000000) if is_number_sum_of_fiths_powers_of_digits(i) and not i is 1])
    print(s)
    assert(s == 443839)

    443839