Tried to solve 55 till 57.

ipython/EulerProblem057.ipynb

@@ -34,6 +34,87 @@
     "In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def get_digit_count(n):\n",
+    "    c = 1\n",
+    "    while n:\n",
+    "        n += 1\n",
+    "        n //= 10\n",
+    "    return d"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def gcd(a, b):\n",
+    "    if b > a:\n",
+    "        a, b = b, a\n",
+    "    while a % b != 0:\n",
+    "        a, b = b, a % b\n",
+    "    return b\n",
+    "        \n",
+    "assert(gcd(100, 35) == 5)\n",
+    "\n",
+    "def add_fractions(n1, d1, n2, d2):\n",
+    "    d = d1 * d2\n",
+    "    n1 = n1 * (d // d1)\n",
+    "    n2 = n2 * (d // d2)\n",
+    "    n = n1 + n2\n",
+    "    p = gcd(n, d)\n",
+    "    return (n // p, d // p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def next_expension(n, d):\n",
+    "    n, d = add_fractions(1, 1, n, d)\n",
+    "    return add_fractions(1, 1, d, n)\n",
+    "\n",
+    "c = 0\n",
+    "\n",
+    "n, d = (3, 2)\n",
+    "for i in range(1000):\n",
+    "    if get_digit_count(n)> get_digit_count(d):\n",
+    "        c += 1\n",
+    "    n, d = next_expension(n, d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "153\n"
+     ]
+    }
+   ],
+   "source": [
+    "s = c\n",
+    "print(s)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,