Solves problem 38 in less than one second.

Code is not that beautiful though.

README.markdown

@@ -47,6 +47,7 @@ Should be used in order to help future reuse of code :)
 35 - How many circular primes are there below one million? <br />
 36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. - 0.933 <br />
 37 - Find the sum of all eleven primes that are both truncatable from left to right and right to left. < 1 min <br />
+38 - What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? < 1 sec <br />
 39 - If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p <= 1000, has the most solutions? - 1min<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 />
@@ -60,8 +61,10 @@ Should be used in order to help future reuse of code :)
 
 26 - Find the value of d < 1000 for which 1/d contains the longest recurring cycle. <br />
 33 - Discover all the fractions with an unorthodox cancelling method. <br />
-38 - What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? <br />
-97 - Find the last ten digits of the non-Mersenne prime: 28433 × 2^7830457 + 1.
+43 - Find the sum of all pandigital numbers with an unusual sub-string divisibility property. <br />
+46 - What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? <br />
+47 - Find the first four consecutive integers to have four distinct primes factors. <br />
+97 - Find the last ten digits of the non-Mersenne prime: 28433 × 2^7830457 + 1. <br />
 
 **WARNING : Spoil inside for those who want to solve problems by themselves :)**
 

e_33.py

@@ -13,4 +13,5 @@ If the product of these four fractions is given in its lowest common terms, find
 ''' 
 
 if __name__ == '__main__':
+    print 1
     #print "Answer : %d " % (last_ten())

e_38.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python 
 '''
-Created on 10 feb. 2012
+Created on 2 may 2012
 
 @author: Julien Lengrand-Lambert
 
@@ -16,7 +16,35 @@ The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5
 
 What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n >1?
 ''' 
+def has_duplicates(mylist):
+    """
+    Returns True if the list contains at least one duplicate
+    """
+    return (len(mylist)!=len(set(mylist)))
+
+def concat_pandigital():
+    """
+    Returns the largest 1 to 9 pandigital number formed as the concatened product of an integer with (1, 2, ..., n)
+    """
+    pand_list = []
+    # max_val is number for which sum(len(max_val * 1) + len(max_val * 2) ) > 9  = 10000
+    for x in range(1, 10000):
+        got = "" # list of all numbers we already have
+        mul = 1
+        doit = 1
+        while doit:
+            cur_val = x * mul
+            if (("0" in str(cur_val)) or (has_duplicates(got + str(cur_val)))):
+                doit = 0
+            else:
+                got += str(cur_val)
+                mul += 1
+        
+        if len(got) == 9: # we have a pandigital number in output
+            print x
+            pand_list.append(int(got)) # should put got back in a correct way
+
+    return max(pand_list)
 
 if __name__ == '__main__':
-    print 1
-    #print "Answer : %d " % (last_ten())
+    print "Answer : %d " % (concat_pandigital())

e_43.py

@@ -0,0 +1,24 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 43 of Project Euler
+The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
+
+Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:
+
+d2d3d4=406 is divisible by 2
+d3d4d5=063 is divisible by 3
+d4d5d6=635 is divisible by 5
+d5d6d7=357 is divisible by 7
+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.
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())

e_46.py

@@ -0,0 +1,24 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 46 of Project Euler
+It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+
+9 = 7 + 2*1^2
+15 = 7 + 2*2^2
+21 = 3 + 2*3^2
+25 = 7 + 2*3^2
+27 = 19 + 2*2^2
+33 = 31 + 2*1^2
+
+It turns out that the conjecture was false.
+
+What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())

e_47.py

@@ -0,0 +1,24 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 47 of Project Euler
+The first two consecutive numbers to have two distinct prime factors are:
+
+14 = 2*7
+15 = 3*5
+
+The first three consecutive numbers to have three distinct prime factors are:
+
+644 = 2^2  7 * 23
+645 = 3 * 5 * 43
+646 = 2  17 * 19.
+
+Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())