148 lines
3.4 KiB
Plaintext
148 lines
3.4 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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"# Permuted multiples (Euler Problem 52)"
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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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"collapsed": true
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},
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"source": [
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"[https://projecteuler.net/problem=52](https://projecteuler.net/problem=52)\n",
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"\n",
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"It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.\n",
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"\n",
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"Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits."
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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": 56,
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"metadata": {},
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"outputs": [],
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"source": [
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"from functools import reduce\n",
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"from operator import eq\n",
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"\n",
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"def get_length(n):\n",
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" \"\"\" Returns the number of digits for n.\n",
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" Returns wrong result for n = 0. \"\"\"\n",
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" length = 0\n",
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" while n:\n",
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" length += 1\n",
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" n //= 10\n",
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" return length\n",
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"\n",
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"assert(get_length(100) == 3)\n",
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"\n",
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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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"assert(get_digits(213) == [3, 1, 2])\n",
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"\n",
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"def get_digits_count(n):\n",
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" digits_count = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
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" for d in get_digits(n):\n",
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" digits_count[d] += 1\n",
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" return digits_count\n",
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"\n",
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"assert(get_digits_count(1258744) == [0, 1, 1, 0, 2, 1, 0, 1, 1, 0])"
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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": 64,
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"metadata": {},
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"outputs": [],
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"source": [
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"def check_if_multiples_contain_same_digits(n, max_multiple=2):\n",
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" n_digits_count = get_digits_count(n)\n",
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" n_length = get_length(n)\n",
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" n_multiple = n * max_multiple\n",
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" while n != n_multiple:\n",
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" if n_length != get_length(n_multiple) or n_digits_count != get_digits_count(n_multiple):\n",
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" return False\n",
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" n_multiple -= n\n",
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" return True\n",
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"\n",
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"assert(check_if_multiples_contain_same_digits(125874))\n",
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"assert(check_if_multiples_contain_same_digits(125875) == False)"
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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": 70,
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"metadata": {},
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"outputs": [],
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"source": [
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"for i in range(1, 10000000):\n",
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" if check_if_multiples_contain_same_digits(i, 6):\n",
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" s = i\n",
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" break"
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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": 72,
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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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"142857\n"
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]
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}
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],
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"source": [
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"print(s)\n",
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"assert(s == 142857)"
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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, 02:32",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python3.6",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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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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"digits",
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"permutations"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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