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problems/006_problem_jnotebook.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#  Problem 6:\n",
+    "\n",
+    "[Euler Project #6](https://projecteuler.net/problem=6)\n",
+    "\n",
+    "> *The sum of the squares of the first ten natural numbers is,\n",
+    "1^2+2^2+...+10^2=385\n",
+    "\n",
+    ">The square of the sum of the first ten natural numbers is,\n",
+    "(1+2+...+10)^2=55^2=3025\n",
+    "\n",
+    ">Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025−385=2640.\n",
+    "\n",
+    ">Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.*\n",
+    "\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Reserved Space For Imports\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import os\n",
+    "import pprint\n",
+    "import time  # Typically imported for sleep function, to slow down execution in terminal.\n",
+    "import typing\n",
+    "import decorators  # Typically imported to compute execution duration of functions.\n",
+    "import numpy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Reserved Space For Method Definition\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def sum_of_squares(i: int,j: int):\n",
+    "    '''\n",
+    "    Function that computes the sum of a series of squared integers.\n",
+    "    '''\n",
+    "    series = [k**2 for k in range(i,j+1)]\n",
+    "    #pprint.pprint(series)\n",
+    "    summ = sum(series)\n",
+    "    return summ"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def square_of_sum(m: int,n: int):\n",
+    "    '''\n",
+    "    Function that computes the square of a summation of a series of integers.\n",
+    "    '''\n",
+    "    series = [p for p in range(m,n+1)]\n",
+    "    summ = sum(series)**2\n",
+    "    #print(summ)\n",
+    "    return summ"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 1. Begin with testing the problem statement's example case.\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Mathematically, the trick is to recognize that this a LCM (Least Common Multiple) problem. The solution is list all the prime factors of each number in the factor list, then compute their collective product.*\n",
+    "\n",
+    " - [ ] Create a method that performs the first computation.\n",
+    " - [ ] Create a method that performs the second computation.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "25164150\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Receive problem inputs...\n",
+    "smallest_factor = 1\n",
+    "largest_factor = 100\n",
+    "\n",
+    "a = square_of_sum(smallest_factor,largest_factor) - sum_of_squares(smallest_factor,largest_factor)\n",
+    "print(a)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "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": "3.8.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}