From 203ea69dbb24ec16de270adead4e4711fe3cd53c Mon Sep 17 00:00:00 2001
From: Julien Lengrand-Lambert <jlengrand@gmail.com>
Date: Sat, 20 Oct 2012 20:00:36 +0200
Subject: [PATCH] Solves problem 43

Starts working on problem 55
---
 README.markdown |  2 +-
 e_43.py         | 53 +++++++++++++++++++++++++++++++++++++++++++++----
 e_55.py         | 28 +++++++++++++++++++++++++-
 3 files changed, 77 insertions(+), 6 deletions(-)

diff --git a/README.markdown b/README.markdown
index 53f6f96..9ec9381 100644
--- a/README.markdown
+++ b/README.markdown
@@ -59,6 +59,7 @@ So you may find some of the code here quite ugly. And this is the case :). Why o
 40 - Finding the nth digit of the fractional part of the irrational number. > 2 sec <br />
 41 - What is the largest n-digit pandigital prime that exists? < 5 min <br />
 42 - Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? - < 1 sec <br />
+43 - Find the sum of all pandigital numbers with an unusual sub-string +divisibility property. - 28sec <br />
 45 - Find the next triangle number that is also pentagonal and hexagonal. - < 1 sec <br />
 46 - What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? - < 6 sec <br />
 48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053 <br />
@@ -70,7 +71,6 @@ So you may find some of the code here quite ugly. And this is the case :). Why o
 
 ## In progress:
 
-43 - Find the sum of all pandigital numbers with an unusual sub-string divisibility property. <br />
 47 - Find the first four consecutive integers to have four distinct primes factors. <br />
 55 - How many Lychrel numbers are there below ten-thousand? <br />
 97 - Find the last ten digits of the non-Mersenne prime: 28433 � 2^7830457 + 1. <br />
diff --git a/e_43.py b/e_43.py
index d52405d..f7afe80 100644
--- a/e_43.py
+++ b/e_43.py
@@ -1,4 +1,4 @@
-#!/usr/bin/env python 
+#!/usr/bin/env python
 '''
 Created on 10 feb. 2012
 
@@ -17,8 +17,53 @@ d6d7d8=572 is divisible by 11
 d7d8d9=728 is divisible by 13
 d8d9d10=289 is divisible by 17
 Find the sum of all 0 to 9 pandigital numbers with this property.
-''' 
+
+Will be very long due to dumb implementation.
+Would be way better with a generator implementation of all_permutations already
+'''
+my_primes = [2, 3, 5, 7, 11, 13, 17]
+
+
+def all_permutations(seq):
+    """permutate a sequence and return a list of the permutations"""
+    if not seq:
+        return [seq]  # is an empty sequence
+    else:
+        temp = []
+        for k in range(len(seq)):
+            part = seq[:k] + seq[k + 1:]
+            for m in all_permutations(part):
+                temp.append(seq[k:k + 1] + m)
+        return temp
+
+
+def is_cool(str_number):
+    """
+    Returns True of number (in a string form) has the cool divisible property
+    """
+    for i in range(len(str_number) - 3):
+        cur = str_number[i + 1:i + 4]
+        if (int(cur) % my_primes[i]) != 0:
+            return False
+    return True
+
+
+def find_cool_pandigital():
+    """
+    Returns the sum of all 0 to 9 pandigital numbers with cool property.
+    """
+    cases = all_permutations("1234567890")
+    cool = []
+    cpt = 0
+    for case in cases:
+        #if int(case[0]) != 0:
+            # check for cool property
+        if is_cool(case):
+            cool.append(int(case))
+
+    print cool
+    print len(cool)
+    return sum(cool)
 
 if __name__ == '__main__':
-    print 1
-    #print "Answer : %d " % (last_ten())
\ No newline at end of file
+    print "Answer : %d " % (find_cool_pandigital())
diff --git a/e_55.py b/e_55.py
index bbd484e..33bc5a9 100644
--- a/e_55.py
+++ b/e_55.py
@@ -42,5 +42,31 @@ the theoretical nature of Lychrel numbers.
  """
 
 
+def reverse(num):
+    """
+    Returns the palidromic number of num
+    """
+    str_num = str(num)
+    rev = ''
+    for i in range(len(str_num)):
+        rev += str_num[len(str_num) - i - 1]
+
+    return int(rev)
+
+
+def count_lychrel(max_num, max_it=50):
+    """
+    Returns the number of lychrel numbers smaller than max_num
+    The maximum iteration number defines how many times the process is repeated
+    before considreing a number to be a lychrel number
+    """
+    lychrels = []
+    for i in xrange(1, max_num + 1):
+        cur = i
+
+    return 1
+
+
 if __name__ == '__main__':
-    print "Answer : %d " % (1)
+    print palindrome(12345)
+    #print "Answer : %d " % (count_lychrel(10000))