Solves problem 56

Didn't expect it to be so simple.

I'd like to find the nice way to sum all numbers of an integer

README.markdown

@@ -12,7 +12,7 @@ The scripts are named as e_problemnumber_inc. The higher the inc, the finer the
 Here is a list of all already solved problems, with a one line explanation.
 Should be used in order to help future reuse of code :)
 
-**Note :** I try to get my solutions within a one minute timeframe. What I want here is to solve problems, not get them running as fast as possible. 
+**Note :** I try to get my solutions within a one minute timeframe. What I want here is to solve problems, not get them running as fast as possible.
 So you may find some of the code here quite ugly. And this is the case :). Why optimize something that completely  fits its purpose ? ;)
 
 
@@ -51,7 +51,7 @@ So you may find some of the code here quite ugly. And this is the case :). Why o
 31 - Investigating combinations of English currency denominations. - < 1 sec <br />
 33 - Discover all the fractions with an unorthodox cancelling method. < 1 sec <br />
 34 - Find the sum of all numbers which are equal to the sum of the factorial of their digits. - 30 sec - 16 sec  <br />
-35 - How many circular primes are there below one million? - **too long** <br /> 
+35 - How many circular primes are there below one million? - **too long** <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 />
@@ -67,8 +67,10 @@ So you may find some of the code here quite ugly. And this is the case :). Why o
 
 ## In progress:
 
+40 - Finding the nth digit of the fractional part of the irrational number. <br />
 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 />
+56 - Considering natural numbers of the form, a^b, finding the maximum digital sum. <br />
 97 - Find the last ten digits of the non-Mersenne prime: 28433 <20> 2^7830457 + 1. <br />
 
 ## Contact

e_40.py

@@ -0,0 +1,21 @@
+#!/usr/bin/env python
+"""
+ ##---
+ # Julien Lengrand-Lambert
+ #Created on : 16 - 10 - 2012
+ #
+ # DESCRIPTION : Solves problem 40 of Project Euler
+ An irrational decimal fraction is created by concatenating the positive integers:
+
+0.123456789101112131415161718192021...
+
+It can be seen that the 12th digit of the fractional part is 1.
+
+If d_n represents the nth digit of the fractional part, find the value of the following expression.
+d_1  d_10  d_100  d_1000  d_10000  d_100000  d_1000000
+
+ ##---
+ """
+ if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())

e_56.py

@@ -0,0 +1,46 @@
+#!/usr/bin/env python
+"""
+ ##---
+ # Julien Lengrand-Lambert
+ #Created on : 16 - 10 - 2012
+ #
+ # DESCRIPTION : Solves problem 56 of Project Euler
+A googol (10^100) is a massive number: one followed by one-hundred zeros;
+100^100 is almost unimaginably large: one followed by two-hundred zeros.
+Despite their size, the sum of the digits in each number is only 1.
+
+Considering natural numbers of the form, a^b, where a, b  100,
+what is the maximum digital sum?
+ ##---
+ """
+
+
+def sum_numbers(val):
+    """
+    Given an value, returns the sum of all its numbers
+    """
+    temp = str(val)
+    res = sum([int(i) for i in temp])
+    return res
+
+
+def sum_pow(max_a, max_b=None):
+    """
+    given val_a and val_b, returns the maximum sum of all numbers of form a^b,
+    where a < max_a and b < max_b
+    If val_b is None, max_a = max_b
+    """
+    if max_b is None:
+        max_b = max_a
+
+    max_val = 0
+    for cur_a in xrange(1, max_a + 1):
+        for cur_b in xrange(1, max_b + 1):
+            cur_val = sum_numbers(pow(cur_a, cur_b))
+            if cur_val > max_val:
+                max_val = cur_val
+    return max_val
+
+
+if __name__ == '__main__':
+    print "Answer : %d " % (sum_pow(100))