{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cycle_length(d):\n",
    "    n = 1\n",
    "    numerators = []\n",
    "\n",
    "    while True:\n",
    "        n *= 10\n",
    "        try:\n",
    "            cycle_start = numerators.index(n)\n",
    "            return len(numerators[cycle_start:])\n",
    "        except ValueError:\n",
    "            numerators.append(n)\n",
    "            n = n % d\n",
    "            if n == 0:\n",
    "                return 0\n",
    "\n",
    "longest_length = 0\n",
    "longest_d = None\n",
    "\n",
    "for d in range(2, 1000):\n",
    "    l = cycle_length(d)\n",
    "    if l > longest_length:\n",
    "        longest_length = l\n",
    "        longest_d = d"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "title": "Reciprocal cycles"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}