Solved 33

frac.py

@@ -0,0 +1,5 @@
+def gcd(a, b):
+    while b:
+        a, b = b, a % b
+
+    return a

problem33.py

@@ -0,0 +1,23 @@
+#!/usr/bin/env python
+from __future__ import division
+from itertools import combinations, permutations
+from frac import gcd
+
+nrs = [(i, str(i)) for i in xrange(10, 100)]
+pairs = ((0, 0), (0, 1), (1, 0), (1, 1))
+
+pn = pd = 1
+
+for (n, ns), (d, ds) in combinations(nrs, 2):
+    if n < d:
+        for i, j in pairs:
+            if ds[1 - j] != '0' and ns[i] == ds[j] \
+                    and int(ns[1 - i]) / int(ds[1 - j]) == n / d \
+                    and ns[1] != '0':
+                pn *= n
+                pd *= d
+                print '%d / %d == %s / %s' % (n, d, ns[1 - i], ds[1 - j])
+
+g = gcd(pn, pd)
+print 'product: %d / %d' % (pn/ g, pd / g)
+print 'answer: %d' % (pd / g)