python.p0074 Namespace Reference

Functions
def	digits
def	main ()

Variables
list	cache = [math.factorial(x) for x in range(10)]

Detailed Description

Project Euler Problem 74

This ended up being a filtering problem. The problem with my solution is that I
am not satisfied with my filter at all. I feel like there is a more efficient
way to go about it.

Problem:

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?

Function Documentation

def python.p0074.digits

(

x

)

Here is the caller graph for this function:

def python.p0074.main

(

int

)

Here is the call graph for this function:

Variable Documentation

list python.p0074.cache = [math.factorial(x) for x in range(10)]