Not cool: Summing factorials of digits

Computer Science Level 3

What is the sum of the first four non-negative numbers with the following property: the number is equal to the sum of the factorials of its digits.

For instance, 23 is NOT such a number, since 2!+3! = 2 + 6 = 8, which is not equal to 23.

The answer is 40733.

2 solutions

Bill Bell
Jan 24, 2015

I did exactly the same thing, except I put the factorials of 0 through 9 in a hash table so it didn't have to calculate factorials over and over again.

Python 2.7:

from math import factorial
fac = {}
for n in xrange(10):
    fac[str(n)] = factorial(n)
def goal(n):
    fac_sum = sum([fac[c] for c in str(n)])
    return n == fac_sum
found = 0
total = 0
n = 0
while found < 4:
    if goal(n):
        found += 1
        total += n
    n += 1
print "Answer:", total

Brock Brown - 6 years, 2 months ago

That's considered good practice, although the numbers involved here are small. (I was too lazy!) Is it possible that you are unaware of memoisation for decorating a function so that its results are saved in case they might be needed again? Here's how I might have used this programming technique for this problem.

Bill Bell - 6 years, 1 month ago

Otavio Monteagudo
Feb 5, 2015

Solution in Python:

def factorial(n): # returns the factorial of that number.
     if (n == 0):
         return 1
     else:
          factorial = 1
          for i in range(1,n+1):
                  factorial *= i
          return factorial

factorial_digits = {}
for i in range(0,10):
    factorial_digits[i] = factorial(i) 
# factorial_digits contains the factorial value for each digit with its original digit as a key

def corresponds_to_sum_of_factorial_digits(n):
    digits = list(str(n))
    summed = 0
    for i in digits:
         summed += factorial_digits[int(i)]
    if (summed == n):
         return True
    return False
    # checks wheter or not the condition specified on the exercise is met.

final_numbers = [] #numbers which follow the condition specified.

# the sum of the factorials from 0 to 9 equals 409114 which has 6 digits, therefore, 6 nested 'for' loops are the maximum needed to solve the problem.

for i in range(0,10): 
    for f in range(0,10):
        for z in range(0,10):
           for g in range(0,10):
               for p in range(0,10):
                   for h in range(0,10):
                       number = int(str(i) + str(f) + str(z) + str(g) + str(p) + str(h))
                       if corresponds_to_sum_of_factorial_digits(number):
                           final_numbers.append(number)
    if (len(final_numbers) == 4):
        break

final_sum = 0

for n in final_numbers:
    final_sum += n

#final_numbers == [1,2,145,40585]
#final_sum == 40733

Not cool: Summing factorials of digits

The answer is 40733.

2 solutions

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