p074.py

# -*- coding: utf-8 -*-
"""
Created on Tue Jul 21 08:13:44 2020

@author: zhixia liu
"""

"""
Project Euler 74: Digit factorial chains

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
"""

#%% naive bf

from math import factorial
from tqdm import tqdm

d = {k:factorial(k) for k in range(10)}

total = 0
for n in tqdm(range(1000000)):
    l = []
    while n not in l:
        l.append(n)
        n = sum([d[int(i)] for i in str(n)])
    if len(l) == 60:
        total += 1
print('\n',total)