Solves Problem 33 (coin change). Adds some new problems

README.markdown

@@ -42,7 +42,9 @@ Should be used in order to help future reuse of code :)
 28 - What is the sum of both diagonals in a 1001 by 1001 spiral? - < 1 sec <br />
 29 - How many distinct terms are in the sequence generated by ab for 2  a  100 and 2  b  100? - < 1 sec <br />
 30 - Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. - < 3 sec <br />
+31 - Investigating combinations of English currency denominations. - < 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? <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 />
@@ -55,8 +57,10 @@ 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 />
+33 - Discover all the fractions with an unorthodox cancelling method. <br />
+37 - Find the sum of all eleven primes that are both truncatable from left to right and right to left. <br />
+38 - What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? <br />
+41 - What is the largest n-digit pandigital prime that exists? <br />
 97 - Find the last ten digits of the non-Mersenne prime: 28433 × 2^7830457 + 1.
 
 **WARNING : Spoil inside for those who want to solve problems by themselves :)**

e_31_2.py

@@ -0,0 +1,40 @@
+#!/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?
+
+This problem is known as the coin change problem.
+''' 
+S = [1, 2, 5, 10, 20, 50, 100, 200] # set of coins
+
+def coin_change(n, m):
+    """
+    Solves the coin change problem for a given set of coins and a desired value.
+    Recursive way
+    """
+    # initial conditions
+    if n == 0 :
+        return 1
+    if n < 0:
+        return 0
+    if m <= 0 and n >= 1 :
+        return 1
+    # either a coin is not in the solution, and can be removed from the set
+    part1 = coin_change(n, m - 1)
+    # or it is part of it, and the final wanted value can be reduced (n - value of the coin)
+    part2 = coin_change(n - S[m], m)
+    return  part1 + part2
+
+if __name__ == '__main__':
+    answer = coin_change(200, len(S) - 1)
+    print "Answer is : %d"  % (answer)
+    

e_33.py

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+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 33 of Project Euler
+The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.
+We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
+There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.
+
+If the product of these four fractions is given in its lowest common terms, find the value of the denominator.
+''' 
+
+if __name__ == '__main__':
+    #print "Answer : %d " % (last_ten())

e_37.py

@@ -0,0 +1,17 @@
+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 37 of Project Euler
+The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
+
+Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
+
+NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())

e_38.py

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+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 38 of Project Euler
+Take the number 192 and multiply it by each of 1, 2, and 3:
+
+192 * 1 = 192
+192 * 2 = 384
+192 * 3 = 576
+By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)
+
+The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).
+
+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?
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())

e_41.py

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+#!/usr/bin/env python 
+'''
+Created on 10 feb. 2012
+
+@author: Julien Lengrand-Lambert
+
+DESCRIPTION: Solves problem 41 of Project Euler
+We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
+
+What is the largest n-digit pandigital prime that exists?
+''' 
+
+if __name__ == '__main__':
+    print 1
+    #print "Answer : %d " % (last_ten())