Solved 44 and 45.

ipython/EulerProblem044.ipynb

@@ -24,6 +24,79 @@
     "Find the pair of pentagonal numbers, $P_j$ and $P_k$, for which their sum and difference are pentagonal and $D = |P_k − P_j|$ is minimised; what is the value of D?"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def pentagonal(n):\n",
+    "    return n * (3 * n - 1) // 2\n",
+    "\n",
+    "assert(pentagonal(1) == 1)\n",
+    "assert(pentagonal(4) == 22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "n = 10000\n",
+    "p = [pentagonal(n) for n in range(1, n)]\n",
+    "p_set = set(p)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Okay, I was honestly just going for plain brute force here and the first solution that came up was the solution to the problem... Not really happy with that."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "i = 1020, j = 2167, d = 5482660.\n"
+     ]
+    }
+   ],
+   "source": [
+    "for i in range(1, n):\n",
+    "    for j in range(i + 1, n):\n",
+    "        if p[i - 1] + p[j - 1] in p_set and p[j - 1] - p[i - 1] in p_set:\n",
+    "            d = pentagonal(j) - pentagonal(i)\n",
+    "            s = d\n",
+    "            print(\"i = {}, j = {}, d = {}.\".format(i, j, d))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5482660\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(s)\n",
+    "assert(s == 5482660)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -35,7 +108,7 @@
   }
  ],
  "metadata": {
-  "completion_date": "",
+  "completion_date": "Sat, 22 Dec 2018, 22:57",
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python3.6",
@@ -53,7 +126,11 @@
    "pygments_lexer": "ipython3",
    "version": "3.6.5"
   },
-  "tags": []
+  "tags": [
+   "pentagonal",
+   "brute force",
+   "improve"
+  ]
  },
  "nbformat": 4,
  "nbformat_minor": 2