Digit factorials : Problem 34 : Project Euler

Digit factorials : Problem 34 Project Euler

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.

To find the upper limit for this problem observe that for a n-digit number the maximum possible  Digit Factorial Sum is 9!*n

For n = 7, Max. Digit Factorial Sum is 9!*7 =2,540,160 which is a 7 digit number

For n = 8, Max. Digit Factorial Sum is 9!*8 =2,903,040 which is a 7 digit number. Hence a the Digit Factorial Sum can never be equal to a 8 digit number! 

Python Code

def digitFactorials():
    def fact(digit):
        l=1
        for i in range(digit):
            l=l*digit
            digit=digit-1
        return l
    number = 10
    sumNumbers = 0
    digitfactsum = 0
    while number < 2540161:
        strnumber = str(number)   
        digitfactsum = 0
        for i in range(len(strnumber)):
            digitfactsum = digitfactsum + fact(int(strnumber[i]))
            if digitfactsum > number:
                break
        if digitfactsum == number:
            sumNumbers = sumNumbers + number
            print number,"Sum of the digits factorials is equal to the number itself"
        number = number + 1
    print "Required Sum is",sumNumbers           
digitFactorials()