Solved 64.

ipython/EulerProblem063.ipynb

@@ -13,11 +13,61 @@
     "collapsed": true
    },
    "source": [
-    "The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.\n",
+    "The 5-digit number, 16807=$7^5$, is also a fifth power. Similarly, the 9-digit number, 134217728=$8^9$, is a ninth power.\n",
     "\n",
     "How many n-digit positive integers exist which are also an nth power?"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_digit_count(n):\n",
+    "    if n < 10:\n",
+    "        return 1\n",
+    "    c = 0\n",
+    "    while n:\n",
+    "        n //= 10\n",
+    "        c += 1\n",
+    "    return c\n",
+    "\n",
+    "assert(get_digit_count(0) == 1)\n",
+    "assert(get_digit_count(1) == 1)\n",
+    "assert(get_digit_count(33) == 2)\n",
+    "assert(get_digit_count(100) == 3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "49\n"
+     ]
+    }
+   ],
+   "source": [
+    "def get_n_digit_positive_integers(n):\n",
+    "    r = []\n",
+    "    i = 1\n",
+    "    while True:\n",
+    "        if get_digit_count(i ** n) == n:\n",
+    "            r.append(i ** n)\n",
+    "        if get_digit_count(i ** n) > n:\n",
+    "            return r\n",
+    "        i += 1\n",
+    "\n",
+    "s = sum([len(get_n_digit_positive_integers(n)) for n in range(1, 1000)])\n",
+    "print(s)\n",
+    "assert(s == 49)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -29,7 +79,7 @@
   }
  ],
  "metadata": {
-  "completion_date": "",
+  "completion_date": "Sun, 6 Jan 2019, 06:17",
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python3.6",
@@ -47,7 +97,9 @@
    "pygments_lexer": "ipython3",
    "version": "3.6.5"
   },
-  "tags": []
+  "tags": [
+   "powers"
+  ]
  },
  "nbformat": 4,
  "nbformat_minor": 2