074.py

'''
Project Euler - Problem 74
http://projecteuler.net/problem=74

Factorial chains...

145 => 1! + 4! + 5! = 1 + 24 + 120 = 145
hence, 145 has a chain with only 1 element

69 => 363600 => 1454 => 169 => 363601 ( => 1454 )
hence, 69 has a chain of 5 elements.

How many numbers below 1 million have a factorial
chain with 60 non-repeating elements?

'''
from math import factorial as fact
from time import time

#counts the length of the factorial chain starting at n
def length(n):
    l=[n]
    m=nxt(n)
    while m not in l:
        l.append(m)
        m=nxt(m)
    return len(l)

#calculates the next term of the factorial chain
nxt = lambda n: sum([fact(int(a)) for a in str(n)])

#start main code here
st=time()
n=1
c=0
while n<=10000:
    if length(n)==60:
        c+=1
        print n,
    n+=1
print c
print time()-st

#output
# 402
# took 5minutes