104 lines
2.3 KiB
Plaintext
104 lines
2.3 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Cubic permutations (Euler Problem 62)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"source": [
|
|
"[https://projecteuler.net/problem=62](https://projecteuler.net/problem=62)\n",
|
|
"\n",
|
|
"The cube, 41063625 (3453), can be permuted to produce two other cubes: 56623104 (3843) and 66430125 (4053). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.\n",
|
|
"\n",
|
|
"Find the smallest cube for which exactly five permutations of its digits are cube."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"cubes = [n * n * n for n in range(1, 5000)]\n",
|
|
"cubes_set = set(cubes)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[127035954683, 352045367981, 373559126408, 569310543872, 589323567104]\n",
|
|
"127035954683\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"solutions = {}\n",
|
|
"\n",
|
|
"for n in range(1, 10000):\n",
|
|
" cube = n * n * n\n",
|
|
" try:\n",
|
|
" key = \"\".join(sorted(str(cube)))\n",
|
|
" solutions[key].append(cube)\n",
|
|
" if len(solutions[key]) > 4:\n",
|
|
" print(solutions[key])\n",
|
|
" s = solutions[key][0]\n",
|
|
" break\n",
|
|
" except KeyError:\n",
|
|
" solutions[key] = [cube]\n",
|
|
"\n",
|
|
"print(s)\n",
|
|
"assert(s == 127035954683)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"completion_date": "Sun, 6 Jan 2019, 05:47",
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python3.6",
|
|
"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": "3.6.5"
|
|
},
|
|
"tags": [
|
|
"cubes"
|
|
]
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|