Add Problem 31 solution

Project Euler/Problem 31/sol1.py

@@ -0,0 +1,53 @@
+# -*- coding: utf-8 -*-
+from __future__ import print_function
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+'''
+Coin sums
+Problem 31
+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, £1 (100p) and £2 (200p).
+It is possible to make £2 in the following way:
+
+1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
+How many different ways can £2 be made using any number of coins?
+'''
+
+
+def one_pence():
+    return 1
+
+
+def two_pence(x):
+    return 0 if x < 0 else two_pence(x - 2) + one_pence()
+
+
+def five_pence(x):
+    return 0 if x < 0 else five_pence(x - 5) + two_pence(x)
+
+
+def ten_pence(x):
+    return 0 if x < 0 else ten_pence(x - 10) + five_pence(x)
+
+
+def twenty_pence(x):
+    return 0 if x < 0 else twenty_pence(x - 20) + ten_pence(x)
+
+
+def fifty_pence(x):
+    return 0 if x < 0 else fifty_pence(x - 50) + twenty_pence(x)
+
+
+def one_pound(x):
+    return 0 if x < 0 else one_pound(x - 100) + fifty_pence(x)
+
+
+def two_pound(x):
+    return 0 if x < 0 else two_pound(x - 200) + one_pound(x)
+
+
+print(two_pound(200))