yaworsw/euler-manager

---
:id: 74
:name: Digit factorial chains
:url: https://projecteuler.net/problem=74
:content: "The number 145 is well known for the property that the sum of the factorial
  of its digits is equal to 145:\n\n1! + 4! + 5! = 1 + 24 + 120 = 145\n\nPerhaps 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:\n\n169 → 363601
  → 1454 → 169  \n871 → 45361 → 871  \n872 → 45362 → 872\n\nIt is not difficult to
  prove that EVERY starting number will eventually get stuck in a loop. For example,\n\n69
  → 363600 → 1454 → 169 → 363601 (→ 1454)  \n78 → 45360 → 871 → 45361 (→ 871)  \n540
  → 145 (→ 145)\n\nStarting 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.\n\nHow many chains, with a starting number below one million, contain
  exactly sixty non-repeating terms?\n\n"