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    "# Euler Problem 28\n",
    "\n",
    "Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:\n",
    "\n",
    "~~~\n",
    "21 22 23 24 25\n",
    "20  7  8  9 10\n",
    "19  6  1  2 11\n",
    "18  5  4  3 12\n",
    "17 16 15 14 13\n",
    "~~~\n",
    "\n",
    "$1 + 3 + 5 + 7 + 9 + 13 + 17 + 21 + 25 = 101$\n",
    "\n",
    "It can be verified that the sum of the numbers on the diagonals is 101.\n",
    "\n",
    "What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?"
   ]
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   "source": [
    "I would try to create a function $f(n)$ which yields the sum of the outmost ring of a n by n spiral.\n",
    "\n",
    "For example:\n",
    "\n",
    "$f(1) = 1$\n",
    "\n",
    "$f(3) = 3 + 5 + 7 + 9 = 24$\n",
    "\n",
    "$f(5) = 13 + 17 + 21 + 25 = 76$\n",
    "\n",
    "When we have this function we calculate the solution simply by\n",
    "\n",
    "~~~\n",
    "s = sum([f(n) for n in range(1, 1002, 2)])\n",
    "~~~\n",
    "\n",
    "For each outer ring there is an initial corner value c ($c_3 = 3, c_5 = 76$). Once we have this value we can caluclate f like $f(n) = c_{n} + (c_n + n - 1) + (c_n + 2(n-1)) + (c_n + 3(n-1)) = 4c_n + 6 (n-1)$"
   ]
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   "source": [
    "def f(n):\n",
    "    if n == 1:\n",
    "        return 1\n",
    "    return 0\n",
    "\n",
    "s = sum([f(n) for n in range(1, 1002, 2)])\n",
    "assert(s == 669171001)\n",
    "s"
   ]
  }
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