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    "#  Problem 9:\n",
    "\n",
    "[Euler Project #9](https://projecteuler.net/problem=9)\n",
    "\n",
    "\n",
    "\n",
    ">A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,\n",
    "a2 + b2 = c2\n",
    "\n",
    ">For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.\n",
    "\n",
    ">There exists exactly one Pythagorean triplet for which a + b + c = 1000.\n",
    "Find the product abc.\n",
    "\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reserved Space For Imports\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "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\n",
    "import pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reserved Space For Method Definition\n",
    "---"
   ]
  },
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   "source": []
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   "source": [
    "## Can we describe a few approaches to solving this problem?\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "*Let's discuss a few ways to work through this, then select one to implement.*\n",
    "\n",
    " 1. Create a 2D array in which we can place each candidate series of integers.\\\n",
    "  A column vector can also be created in which can store the product of each series.\\\n",
    "  If we zip these arrays together, sort on the product column, we can identify the\\\n",
    "  the maximum product and its associate string of integers.\n",
    "<br/>\n",
    "<br/>\n",
    " 2. Create an array (of the specified length) to store a series of integers from the input\\\n",
    "  number. Allow this to be an array that we use to compute the a product. It will shift as we\\\n",
    "  slide along the input number. A second array of identical dimension, plus an additional place,\\\n",
    "  could store the largest product, and the associated list of integers.  \n",
    " "
   ]
  },
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   "source": [
    "### Let's try the first approach!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. a) Take in problem statement information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. b) Build out the candidate array. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. c) Cheat by using pandas to print out the maximum product and its associated series of integers. "
   ]
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