Finished 32 in ipython.

ipython/EulerProblem032.ipynb

@@ -15,6 +15,13 @@
     "HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We start by thinking about how many digits are used for multiplicand/multiplier/product. Obviously, the product must have more then three digits. Can it have more then 4 digits? Obviously it can because then there are only four digits for multiplicand and multiplier which is always smaller than ten thousand. So our product must be in the form $12 \\cdot 345 = 5789$. This makes the rest very easy in Python."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 1,
@@ -23,30 +30,36 @@
    },
    "outputs": [
     {
-     "ename": "AssertionError",
-     "evalue": "",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
-      "\u001b[1;32m<ipython-input-1-8e612cf3c592>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m45228\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[1;31mAssertionError\u001b[0m: "
-     ]
+     "data": {
+      "text/plain": [
+       "45228"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "s = 0\n",
-    "assert(s == 45228)"
+    "from itertools import permutations\n",
+    "\n",
+    "def is_solution(s):\n",
+    "    a, b, c = int(s[0:2]), int(s[2:5]), int(s[5:])\n",
+    "    if a * b == c:\n",
+    "        return c\n",
+    "    a, b, c = int(s[0:1]), int(s[1:5]), int(s[5:])  \n",
+    "    if a * b == c:\n",
+    "        return c\n",
+    "    return 0\n",
+    "\n",
+    "assert(is_solution(\"391867254\") == 7254)\n",
+    "assert(is_solution(\"391867245\") == 0)\n",
+    "\n",
+    "\n",
+    "s = sum(set([is_solution(\"\".join(p)) for p in permutations(\"123456789\")]))\n",
+    "assert(s == 45228)\n",
+    "s"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {