new_contents: #
  # This is a ridiculously slow solution. Also the cache is pointless (stupid)
  # as-is, it would most likely be VERY much smarter to cache the number or divisors for
  # each number (any number) and then use these cached values inside the divisors() function
  #
  # Running this code until the answer is printed takes between 8 and 18 hours.
  #
  # Answer was: 76576500 which is the 12375'th triangle number
  # This number has has 576 divisors.
  #
  
  
  
  import math
  
  MINIMUM_DIVISOR_COUNT = 500
  
  
  # returns the Nth triangle number
  def triangle_number_old_slow(n):
  	sum = 0
  	for i in xrange(1,n + 1):
  		sum += i
  	return sum
  
  def triangle_number(n):
  	return (n + 1) * n / 2
  
  # unit tests
  assert triangle_number(7) == 28
  
  # returns the set of all integers that divides "n"
  def divisors(n):
  	return filter(lambda d: n % d == 0, xrange(1, n + 1))
  
  def divisor_count_for_triangle_number(n):
  	cached_value = divisor_count_cache.get(n, -1)
  	if cached_value != -1:
  		return cached_value
  	divisor_count_cache[n] = len(divisors(triangle_number(n)))
  	return divisor_count_for_triangle_number(n)
  
  divisor_count_cache = {}
  div_count = 0
  number = 1
  while div_count < MINIMUM_DIVISOR_COUNT:
  	number += 1
  	div_count = divisor_count_for_triangle_number(number)
  	print "triangle number", number, "is", triangle_number(number), "and has", div_count, "divisors"
  print
  print
  print "triangle number", number, "is", triangle_number(number), "and has more than", MINIMUM_DIVISOR_COUNT, "divisors"
  
subject: add SLOW python solution for "project euler - problem 12"