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"""

Problem 34: https://projecteuler.net/problem=34

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: As 1! = 1 and 2! = 2 are not sums they are not included.

"""

from math import factorial

def sum_of_digit_factorial(n: int) -> int:

"""

Returns the sum of the digits in n

>>> sum_of_digit_factorial(15)

121

>>> sum_of_digit_factorial(0)

"""

return sum(factorial(int(char)) for char in str(n))

def solution() -> int:

"""

Returns the sum of all numbers whose

sum of the factorials of all digits

add up to the number itself.

>>> solution()

40730

"""

limit = 7 * factorial(9) + 1

return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)

if __name__ == "__main__":

print(f"{solution()} = ")

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