move notebooks to subdir

notebooks/problem0004.ipynb

@@ -0,0 +1,60 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "9c7a281d",
+   "metadata": {},
+   "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))"
+   ]
+  }
+ ],
+ "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
+}