133 lines
2.7 KiB
Plaintext
133 lines
2.7 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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"# Triangular, pentagonal, and hexagonal (Euler Problem 45)"
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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=45](https://projecteuler.net/problem=45)\n",
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"\n",
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"Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:\n",
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"\n",
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"Triangle\t \t$T_n=n(n+1)/2 = 1, 3, 6, 10, 15, ...$\n",
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"\n",
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"Pentagonal\t \t$P_n=n(3n−1)/2 = 1, 5, 12, 22, 35, ...$\n",
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"\n",
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"Hexagonal\t \t$H_n=n(2n−1) = 1, 6, 15, 28, 45, ...$\n",
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"\n",
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"It can be verified that T285 = P165 = H143 = 40755.\n",
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"\n",
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"Find the next triangle number that is also pentagonal and hexagonal."
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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 T(n):\n",
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" return n * (n + 1) // 2\n",
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"\n",
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"assert(T(3) == 6)\n",
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"\n",
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"def P(n):\n",
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" return n * (3 * n - 1) // 2\n",
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"\n",
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"assert(P(3) == 12)\n",
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"\n",
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"def H(n):\n",
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" return n * (2 * n - 1)\n",
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"\n",
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"assert(H(3) == 15)"
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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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"n_max = 100000\n",
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"s = 0\n",
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"\n",
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"T_list = [T(n) for n in range(1, n_max + 1)]\n",
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"P_set = {P(n) for n in range(1, n_max + 1)}\n",
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"H_set = {H(n) for n in range(1, n_max + 1)}\n",
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"\n",
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"for n in range(1, n_max + 1):\n",
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" if T_list[n - 1] in P_set and T_list[n - 1] in H_set:\n",
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" t = T_list[n - 1]\n",
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" if t > 40755:\n",
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" 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": 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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"1533776805\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 == 1533776805)"
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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": "Sat, 22 Dec 2018, 23:17",
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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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"triangular",
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"pentagonal",
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"hexagonal"
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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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