Project Euler Problem 30

Problem 30

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.

# 寻找一些数，他们各位数的5次方相加等于自身，求这些数的和。

i = 2
sum1 = 0
while i < 360000:
    string = str(i)
    l = [(int(x))**5 for x in string]
    if i == sum(l):
        print(i)
        sum1 += i
    i += 1
print(sum1)

思路：如果这个数为7位数，它一定小于7*9！=413343，所以这样的数不会是7位数或更大

         如果这个数为6位数，它一定小于6*9！=354294，所以搜索上界就是它

结果：443839