{
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  {
   "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": [],
   "source": [
    "from itertools import count\n",
    "\n",
    "def is_pandigital(s):\n",
    "    return ''.join(sorted(s)) == \"123456789\"\n",
    "\n",
    "\n",
    "pandigitals = dict()\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[k] = int(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6fe58cf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 123456789,\n",
       " 9: 918273645,\n",
       " 192: 192384576,\n",
       " 219: 219438657,\n",
       " 273: 273546819,\n",
       " 327: 327654981,\n",
       " 6729: 672913458,\n",
       " 6792: 679213584,\n",
       " 6927: 692713854,\n",
       " 7269: 726914538,\n",
       " 7293: 729314586,\n",
       " 7329: 732914658,\n",
       " 7692: 769215384,\n",
       " 7923: 792315846,\n",
       " 7932: 793215864,\n",
       " 9267: 926718534,\n",
       " 9273: 927318546,\n",
       " 9327: 932718654}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandigitals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "faf514b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "932718654"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(pandigitals.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "094c440b",
   "metadata": {},
   "source": [
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
   ]
  }
 ],
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