Mr. Warner.py

#!/usr/bin/env python
"""
Yasyf Mohamedali (http://www.yasyf.com)
First published at https://gist.github.com/yasyf/5299301

A quick python script to solve the math riddle involving an insurance broker and a woman's daughters. 
This script will take a variable amount of daughters, whose ages multiply to any number, and present you with all possible solutions, if any.

Quickstart:
	To run, save the script, make sure you have python installed, and simply run the following from the command line:
		python 'Mr. Warner.py'
"""

import math, itertools, collections

def get_int(prompt):
	print prompt
	return input("> ")

def find_factors(n):
	sqrt = math.sqrt(n)
	i = 1
	factors = []
	while i <= sqrt:
		if n % i == 0:
			factors.append(i)
			if i != sqrt:
				factors.append(n/i)
		i += 1
	return sorted(factors)

def product_combination(combination):
	product = 1
	for i in range(0,len(combination)):
		product *= combination[i]
	return product

def sum_combination(combination):
	sum = 0
	for i in range(0,len(combination)):
		sum += combination[i]
	return sum
		
def possible_combinations(n,product,factors):
	return [x for x in itertools.combinations_with_replacement(factors, n) if product_combination(x) == product]
		
def combinations_with_repeated_sums(combinations):
	sums = dict(zip([x for x in combinations],[sum_combination(x) for x in combinations]))
	repeated_sums = [x for x,y in collections.Counter(sums.values()).items() if y > 1]
	return [x for x in sums.keys() if sums[x] in repeated_sums]

def filter_single_oldest(combinations):
	return [x for x in combinations if x[-1] != x[-2]]

def format_children(combination):
	response = "The ages of the %s children are " % len(combination)
	for x in combination:
		if x == 1:
			addition = "1 year old"
		else:
			addition = "%s years old" % x
		if x == combination[len(combination)-1]:
			response += "and %s." % addition
		else:
			response += "%s, " % addition
	return response
		

def print_answers(combinations):
	if len(combinations) == 0:
		print "There is no solution to this question."
	elif len(combinations) == 1:
		print format_children(combinations[0])
	else:
		print "There are %s possible answers:" % len(combinations)
		for x in combinations:
			print format_children(x)
		
def run(number_children=None,age_product=None):
	if number_children is None:
		number_children = get_int("How Many Children?")
	if age_product is None:
		age_product = get_int("What Is The Product Of Their Ages?")
	#each age must be a factor of (the product of the ages)
	#find all the factors of (the product of the ages) 
	factors = find_factors(age_product)
	#find every possible combination of choosing the a certain number of ages (the number of children) from all the factors of (the product of the ages)
	#for example, if there are three children, find all the possible combinations of choosing three ages from the list of all the factors
	combinations = possible_combinations(number_children,age_product,factors)
	#since the man didn't have enough information after the first clue, there must be multiple combinations that add up to the same number (the house next door)
	#for each combination, sum up the ages, and find the combinations that correspond with sums that are repeated at least twice
	repeats = combinations_with_repeated_sums(combinations)
	#since there is only one eldest child, the two eldest children cannot have the same age
	#filter out any answers where the two eldest children have the same age
	valid_answers = filter_single_oldest(repeats)
	#print the answers, if any
	print_answers(valid_answers)
	
	return len(valid_answers)
		
def find_result(n,strict=True,x=1,y=1):
#find numbers that give n results
	found = False
	while found is False:
		if x >= 5:
			x = 1
			y += 1
		else:
			x += 1
		print "Testing with %s children whose ages multiply to %s." % (x,y) 
		result = run(x,y)
		if (result == n) or (result > n and strict is False):
			print "There are %s solutions with %s children whose ages multiply to %s." % (result,x,y)
			found = True	
				
def main():
	run()
	#find_result(3)
	
	
if __name__ == '__main__':
    main()

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