Drafted solution for 53 and 54. I will have to validate.

ipython/EulerProblem053.ipynb

@@ -30,6 +30,58 @@
     "How many, not necessarily distinct, values of  nCr, for 1 ≤ n ≤ 100, are greater than one-million?"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "\n",
+    "def combinations_naiv(n, r):\n",
+    "    return math.factorial(n) // (math.factorial(r) * math.factorial(n - r))\n",
+    "\n",
+    "assert(combinations_naiv(5, 3) == 10)\n",
+    "assert(combinations_naiv(23, 10) == 1144066)\n",
+    "assert(combinations_naiv(20, 20) == 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "count = 0\n",
+    "\n",
+    "for n in range (1, 101):\n",
+    "    for r in range(1, n + 1):\n",
+    "        if combinations_naiv(n, r) > 10**6:\n",
+    "            count += 1\n",
+    "\n",
+    "s = count"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4075\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(s)\n",
+    "assert(s == 4075)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,