add more info about the answer

notebooks/problem0039.ipynb

@@ -43,7 +43,7 @@
    "id": "431ef21c",
    "metadata": {},
    "source": [
-    "Now we can just iterate through our new generator and count the perimeters. We also count multiples of the perimeters to include non-primitive triplets."
+    "Now we can just iterate through our new generator and group each triangle by their perimeters. We also multiply to consider non-primitive triplets."
    ]
   },
   {
@@ -53,6 +53,34 @@
    "metadata": {
     "scrolled": true
    },
+   "outputs": [],
+   "source": [
+    "max_perim = 1000\n",
+    "perimeters = dict()\n",
+    "for (a, b, c) in primitive_pythagorean_triplets(max_perim):\n",
+    "    for k in count(1):\n",
+    "        perimeter = k * (a + b + c)\n",
+    "        if perimeter > max_perim:\n",
+    "            break\n",
+    "        \n",
+    "        if perimeter not in perimeters:\n",
+    "            perimeters[perimeter] = set()\n",
+    "        perimeters[perimeter].add((k*a, k*b, k*c))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f776a5c6",
+   "metadata": {},
+   "source": [
+    "Our answer is whichever perimeter has the highest total."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "0cd6241f",
+   "metadata": {},
    "outputs": [
     {
      "data": {
@@ -60,25 +88,50 @@
        "840"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "from collections import Counter\n",
-    "\n",
-    "max_perim = 1000\n",
-    "perimeters = Counter()\n",
-    "for (a, b, c) in primitive_pythagorean_triplets(max_perim):\n",
-    "    for k in count(1):\n",
-    "        perimeter = k * (a + b + c)\n",
-    "        if perimeter > max_perim:\n",
-    "            break\n",
-    "        \n",
-    "        perimeters[perimeter] += 1\n",
-    "\n",
-    "max(perimeters, key=perimeters.get)"
+    "p = max(perimeters, key=lambda x: len(perimeters[x]))\n",
+    "p"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f32fb164",
+   "metadata": {},
+   "source": [
+    "There are eight triangles with this perimeter."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "9c31c68f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(105, 360, 375),\n",
+       " (140, 336, 364),\n",
+       " (210, 280, 350),\n",
+       " (252, 240, 348),\n",
+       " (315, 168, 357),\n",
+       " (350, 120, 370),\n",
+       " (390, 56, 394),\n",
+       " (399, 40, 401)}"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "perimeters[p]"
    ]
   },
   {