Brute forcing a menacing maths problem

sumperms1234.ipynb

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    "[Referencing this blog post](https://medium.com/@fjmubeen/my-nephew-brought-home-this-menacing-maths-problem-e8bbba30e5cb#.79es8wsz2)\n",
    "\n",
    "How many combinations are there?"
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   "source": [
    "import math\n",
    "math.factorial(4)**4"
   ]
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    "Few enough to brute force :)"
   ]
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   "source": [
    "from itertools import product, permutations\n",
    "\n",
    "# converts a list of ditits to the base 10 integer\n",
    "to_num = lambda digits: sum(map(lambda (i, n): n*10**i, enumerate(reversed(digits))))\n",
    "\n",
    "# all numbers that are permutations of the digits\n",
    "perms = map(to_num, permutations([1,2,3,4]))\n",
    "\n",
    "# all combinations of four of those numbers (itertools.product is Cartesian product)\n",
    "combos = product(*[perms]*4)\n",
    "\n",
    "# sum them\n",
    "sums = map(sum, combos)"
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      "True\n",
      "True\n"
     ]
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   "source": [
    "# sanity checks\n",
    "print len(sums) == math.factorial(4)**4\n",
    "print (1234*4, 4321*4) == (min(sums), max(sums))"
   ]
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    "9000 in sums"
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