160 lines
4.4 KiB
Plaintext
160 lines
4.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Lychrel numbers (Euler Problem 55)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"source": [
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"[https://projecteuler.net/problem=55](https://projecteuler.net/problem=55)\n",
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"\n",
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"If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.\n",
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"\n",
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"Not all numbers produce palindromes so quickly. For example,\n",
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"\n",
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"$349 + 943 = 1292$\n",
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"\n",
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"$1292 + 2921 = 4213$\n",
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"\n",
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"$4213 + 3124 = 7337$\n",
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"\n",
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"That is, 349 took three iterations to arrive at a palindrome.\n",
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"\n",
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"Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).\n",
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"\n",
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"Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.\n",
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"\n",
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"How many Lychrel numbers are there below ten-thousand?\n",
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"\n",
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"NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def get_digits(n):\n",
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" d = []\n",
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" while n:\n",
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" d.append(n % 10)\n",
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" n //= 10\n",
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" return d\n",
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"\n",
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"def is_pilandrome(n):\n",
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" ds = get_digits(n)\n",
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" len_ds = len(ds)\n",
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" if len_ds < 2:\n",
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" return True\n",
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" for i in range(0, len_ds // 2):\n",
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" if ds[i] != ds[len_ds - i - 1]:\n",
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" return False\n",
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" return True\n",
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"\n",
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"assert(is_pilandrome(1337) == False)\n",
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"assert(is_pilandrome(1331))\n",
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"assert(is_pilandrome(131))\n",
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"assert(is_pilandrome(132) == False)\n",
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"\n",
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"\n",
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"def get_digit_inverse(n):\n",
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" ds = get_digits(n)\n",
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" base = 1\n",
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" i = 0\n",
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" for d in ds[::-1]:\n",
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" i += (base * d)\n",
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" base *= 10\n",
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" return i\n",
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"\n",
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"assert(get_digit_inverse(47) == 74)\n",
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"assert(get_digit_inverse(47) == 74)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def is_not_lychrel(n, iterations=50):\n",
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" for i in range(0, iterations):\n",
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" n = n + get_digit_inverse(n)\n",
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" if is_pilandrome(n):\n",
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" return (i + 1)\n",
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" return 0\n",
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"\n",
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"assert(is_not_lychrel(47) == 1)\n",
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"assert(is_not_lychrel(349) == 3)\n",
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"assert(is_not_lychrel(10677, 100) == 53)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"249\n"
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]
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}
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],
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"source": [
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"lychrels = [n for n in range(1, 10000) if is_not_lychrel(n) == 0]\n",
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"s = len(lychrels)\n",
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"print(s)\n",
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"assert(s == 249)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"completion_date": "Mon, 24 Dec 2018, 23:32",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.6",
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"pygments_lexer": "ipython3",
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"version": "3.6.5"
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},
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"tags": [
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"lychrel",
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"airplane"
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