add problem 38

notebooks/problem0038.ipynb

@@ -0,0 +1,74 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d5ba1893",
+   "metadata": {},
+   "source": [
+    "# [Pandigital Multiples](https://projecteuler.net/problem=38)\n",
+    "\n",
+    "Any number with five or more digits will have a concatenated product with more than 9 digits. Therefore we only need to check numbers with less than five digits."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "ffea7112",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "932718654"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from itertools import count\n",
+    "\n",
+    "def is_pandigital(s):\n",
+    "    return ''.join(sorted(s)) == \"123456789\"\n",
+    "\n",
+    "\n",
+    "pandigitals = set()\n",
+    "for k in range(1, 10000):\n",
+    "    s = \"\"\n",
+    "    for n in count(1):\n",
+    "        s += str(k * n)\n",
+    "        if len(s) >= 9:\n",
+    "            break\n",
+    "    \n",
+    "    if is_pandigital(s):\n",
+    "        pandigitals.add(int(s))\n",
+    "\n",
+    "        \n",
+    "max(pandigitals)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}