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  {
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   "source": [
    "# [Largest Palindrome Product](https://projecteuler.net/problem=4)\n",
    "\n",
    "Our search space is only $\\binom{900}{2} = 404550$ 3-digit pairs - a lot to check by hand but peanuts to a modern computer (we're using notation for [combinations](https://en.wikipedia.org/wiki/Combination) if you're unfamiliar)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e5fd66f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "906609"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import combinations\n",
    "\n",
    "is_palindrome = lambda x: str(x) == str(x)[::-1]\n",
    "three_digit_pairs = combinations(range(100, 1000), 2)\n",
    "max(x*y for (x,y) in three_digit_pairs if is_palindrome(x*y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac68b4da",
   "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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