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   "source": [
    "#  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,
   "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 math\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reserved Space For Method Definition\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_c(a,b):\n",
    "    c = math.sqrt(a*a+b*b)\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_constraint(a,b,c,limit):\n",
    "    return (a+b+c)==limit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Brute Force!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200 375 425.0 1000.0 31875000.0\n"
     ]
    }
   ],
   "source": [
    "exit=False\n",
    "for a in range(1,1000):\n",
    "    for b in range(a,1000):\n",
    "        c = get_c(a,b)\n",
    "        if check_constraint(a,b,c,1000):\n",
    "            #print(a,b,c)\n",
    "            #print(not_done)\n",
    "            exit=True\n",
    "            break\n",
    "    if exit:\n",
    "        break\n",
    "print(a,b,c,a+b+c,a*b*c)\n"
   ]
  }
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