153 lines
3.4 KiB
Plaintext
153 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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"id": "24453968",
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"metadata": {},
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"source": [
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"# [Cube Digit Pairs](https://projecteuler.net/problem=90)\n",
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"\n",
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"There's only ${10 \\choose 6} = 210$ distinct cubes, making this problem easy to brute force. We first make a generator for those cubes."
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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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"id": "06b0661f",
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"metadata": {},
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"outputs": [],
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"source": [
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"from itertools import combinations\n",
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"\n",
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"def cubes():\n",
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" yield from combinations(range(0, 10), 6)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "87ba05f8",
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"metadata": {},
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"source": [
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"We also write a simple function for handling the fact that we can flip 6s and 9s."
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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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"id": "15dab5dd",
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"metadata": {},
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"outputs": [],
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"source": [
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"def extended_set(s):\n",
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" s = set(s)\n",
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" if 6 in s:\n",
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" s.add(9)\n",
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" elif 9 in s:\n",
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" s.add(6)\n",
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" \n",
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" return s"
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]
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},
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{
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"cell_type": "markdown",
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"id": "42f875d0",
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"metadata": {},
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"source": [
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"Another simple function tests if we can display all the square numbers with a given pair of cubes."
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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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"id": "7396b4e8",
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"metadata": {},
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"outputs": [],
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"source": [
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"def all_squares_displayable(s, t):\n",
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" es = extended_set(s)\n",
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" et = extended_set(t)\n",
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" \n",
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" square_digits = ((0, 1), (0, 4), (0, 9), (1, 6), (2, 5), (3, 6), (4, 9), (6, 4), (8, 1))\n",
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" for (m, n) in square_digits:\n",
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" if not ((m in es and n in et) or (n in es and m in et)):\n",
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" return False\n",
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" \n",
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" return True"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9efa8055",
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"metadata": {},
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"source": [
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"Then we just check all the cube pairs."
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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": 4,
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"id": "2d11c86f",
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"metadata": {},
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"outputs": [],
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"source": [
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"arrangements = set()\n",
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"for s, t in combinations(cubes(), 2):\n",
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" if all_squares_displayable(s, t):\n",
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" arrangements.add((s, t))"
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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": 5,
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"id": "8ce1fab4",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1217"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"len(arrangements)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7229398d",
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"metadata": {},
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"source": [
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"#### Copyright (C) 2025 filifa\n",
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"\n",
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"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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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": "3.11.2"
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}
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"nbformat": 4,
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"nbformat_minor": 5
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