From ee38e14979eeb7357fc818e1e5ed15195a9cf17f Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Sun, 25 May 2025 23:12:08 -0400
Subject: [PATCH] add problem 55

---
 notebooks/problem0055.ipynb | 105 ++++++++++++++++++++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 notebooks/problem0055.ipynb

diff --git a/notebooks/problem0055.ipynb b/notebooks/problem0055.ipynb
new file mode 100644
index 0000000..550d114
--- /dev/null
+++ b/notebooks/problem0055.ipynb
@@ -0,0 +1,105 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "de629cc8",
+   "metadata": {},
+   "source": [
+    "# [Lychrel Numbers](https://projecteuler.net/problem=55)\n",
+    "\n",
+    "This could get tricky if we were working with fixed size integers, since the reverse-and-add process for [Lychrel numbers](https://en.wikipedia.org/wiki/Lychrel_number) can result in some big numbers. But Python ints have unlimited precision, so no need to worry about that."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "5588d5d2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def is_palindrome(n):\n",
+    "    s = str(n)\n",
+    "    return s == s[::-1]\n",
+    "\n",
+    "\n",
+    "def is_lychrel_number(n):\n",
+    "    for _ in range(0, 50):\n",
+    "        rev = int(str(n)[::-1])\n",
+    "        n += rev\n",
+    "        if is_palindrome(n):\n",
+    "            return False\n",
+    "        \n",
+    "    return True"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d45f3460",
+   "metadata": {},
+   "source": [
+    "This is easy to brute force, since we're not checking that many numbers, and we loop at most 50 times in our test."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "e473996a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "lychrel_numbers = {n for n in range(1, 10000) if is_lychrel_number(n)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "2c3f1cbf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "249"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(lychrel_numbers)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ef8a3b03",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Suspected Lychrel numbers: [A023108](https://oeis.org/A023108)"
+   ]
+  }
+ ],
+ "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
+}