output a little more info

notebooks/problem0032.ipynb

@@ -17,24 +17,13 @@
    "execution_count": 1,
    "id": "5d61d14d",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "45228"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "def is_pandigital(n):\n",
     "    return ''.join(sorted(n)) == \"123456789\"\n",
     "\n",
     "\n",
-    "products = set()\n",
+    "products = dict()\n",
     "for p in range(1, 10000):\n",
     "    for q in range(p, 10000):\n",
     "        product = p * q\n",
@@ -44,9 +33,65 @@
     "            break\n",
     "            \n",
     "        if is_pandigital(s):\n",
-    "            products.add(product)\n",
-    "\n",
-    "sum(products)"
+    "            products[(p, q)] = product"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "bd9cd5ec",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(4, 1738): 6952,\n",
+       " (4, 1963): 7852,\n",
+       " (12, 483): 5796,\n",
+       " (18, 297): 5346,\n",
+       " (27, 198): 5346,\n",
+       " (28, 157): 4396,\n",
+       " (39, 186): 7254,\n",
+       " (42, 138): 5796,\n",
+       " (48, 159): 7632}"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "products"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3dfd3706",
+   "metadata": {},
+   "source": [
+    "As the problem hinted, some of these products appear more than once, but we only count each once in our sum."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f63472a3",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "45228"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(set(products.values()))"
    ]
   }
  ],