Solves Problem 39. 1 minute time is reached, but the solution comes up

to be very ugly. 
I'm sure I can find something better than that !

Still have to perform some good work on prime numbers! (one day . . . )
I begin to lack some primes problems cause of that :s 

Signed-off-by: Julien Lengrand-Lambert <julien@lengrand.fr>

README.markdown

@@ -1,4 +1,4 @@
-#My solutions to Project Euler 's website
+ #My solutions to Project Euler 's website
 
 [Project Euler](http://projecteuler.net/) is a website containing lots of problems aiming at being solved.
 I play around with them in order to sharpen my algorithm skills. 
@@ -44,6 +44,7 @@ Should be used in order to help future reuse of code :)
 30 - Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. - < 3 sec <br />
 34 - Find the sum of all numbers which are equal to the sum of the factorial of their digits. - 30 sec  <br />
 36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. - 0.933 <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 />
 42 - Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? - < 1 sec <br />
 45 - Find the next triangle number that is also pentagonal and hexagonal. - < 1 sec <br /> 
 48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053 <br />
@@ -53,8 +54,9 @@ Should be used in order to help future reuse of code :)
 **In progress: **
 
 26 - Find the value of d < 1000 for which 1/d contains the longest recurring cycle. <br />
+31 - Investigating combinations of English currency denominations. <br />
 35 - How many circular primes are there below one million? <br />
-39 - If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p <= 1000, has the most solutions? <br />
+53 - How many values of C(n,r), for 1 <= n <= 100, exceed one-million? <br />
 
 **WARNING : Spoil inside for those who want to solve problems by themselves :)**
 

e_31.py

@@ -0,0 +1,23 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 31 of Project Euler
+In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:
+
+1p, 2p, 5p, 10p, 20p, 50p, L1 (100p) and L2 (200p).
+It is possible to make L2 in the following way:
+
+1 * L1 + 1 * 50p + 2 * 20p + 1 * 5p + 1 * 2p + 3 * 1p
+How many different ways can L2 be made using any number of coins?
+''' 
+def aaa():
+    """
+    Returns 
+    """
+    return 1
+
+if __name__ == '__main__':
+    print "Answer : %d " % (1)

e_39.py

@@ -11,14 +11,53 @@ If p is the perimeter of a right angle triangle with integral length sides, {a,b
 
 For which value of p  1000, is the number of solutions maximised?
 ''' 
-def sum_power():
+def per_tri(max_per):
     """
-    Finds
+    Returns the maximum number of solutions maximised for a given max value of perimeter.  
     """
+    max_sol = 0
+    max_p = 0
+    for p in range(3, max_per + 1):
+        print "%d/%d" %(p, max_per + 1)
+        nb_sol = 0
+        sols = []
+        for a in range(1, p):
+            for b in range(1, p - a):
+                c = p - a - b
+                if is_rect(a, b, c):
+                    if is_present([a, b, c], sols):
+                        pass
+                    else:
+                        sols.append([a, b, c])
+                        nb_sol += 1
         
+        if nb_sol > max_sol:
+            max_sol = nb_sol
+            max_p = p
             
-    return 1
+    return max_p
+
+def is_present(cur_sol, sols):
+    """
+    Returns True if solution is already in the list
+    """
+    for sol in sols:
+        val = 0
+        for side in cur_sol:
+            if side in sol:
+                val += 1
+        
+        if val == len(cur_sol):
+            return True
+    
+    return False
+
+def is_rect(a, b, c):
+    """
+    Returns true if the triangle is rectangle, c being the hypothenuse.
+    """
+    return (a**2 + b**2 == c**2)
 
 if __name__ == '__main__':
-    # The major problem in there is to find the upper limit.  
-    print "Answer : %d " % (sum_power())
+    # really ugly solution!
+    print "Answer : %d " % (per_tri(1000))

e_53.py

@@ -0,0 +1,28 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 53 of Project Euler
+There are exactly ten ways of selecting three from five, 12345:
+
+123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
+
+In combinatorics, we use the notation, 5C3 = 10.
+
+In general,
+
+nCr = n! / r!(nr)! ,where r  n, n! = n(n1)...321, and 0! = 1.
+It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
+
+How many, not necessarily distinct, values of  nCr, for 1  n  100, are greater than one-million?
+''' 
+def aaa():
+    """
+    Returns 
+    """
+    return 1
+
+if __name__ == '__main__':
+    print "Answer : %d " % (1)