Euler 043 - Sub-string divisibility.ipynb

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    "Euler Problem 43\n",
    "================\n",
    "\n",
    "The number 1406357289 is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.\n",
    "\n",
    "Let $d_1$ be the 1st digit, $d_2$ be the 2nd digit, and so on. In this way, we note the following:\n",
    "\n",
    "+ $d_2d_3d_4=406$ is divisible by 2\n",
    "+ $d_3d_4d_5=063$ is divisible by 3\n",
    "+ $d_4d_5d_6=635$ is divisible by 5\n",
    "+ $d_5d_6d_7=357$ is divisible by 7\n",
    "+ $d_6d_7d_8=572$ is divisible by 11\n",
    "+ $d_7d_8d_9=728$ is divisible by 13\n",
    "+ $d_8d_9d_{10}=289$ is divisible by 17\n",
    "\n",
    "Find the sum of all 0 to 9 pandigital numbers with this property."
   ]
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      "16695334890\n"
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   "source": [
    "def f(v = (), len_v = 0):\n",
    "    primes = [2, 3, 5, 7, 11, 13, 17]\n",
    "    if len_v == 0 or (not(v[-1] in v[:-1]) and (len_v < 4 or (v[-3]*100 + v[-2]*10 + v[-1]) % primes[len(v)-4] == 0)):\n",
    "        if len_v == 10:\n",
    "            yield v\n",
    "        else:\n",
    "            for d in range(10):\n",
    "                for w in f(v+(d,), len_v + 1):\n",
    "                    yield w\n",
    "\n",
    "print(sum(sum(v[i]*10**(9-i) for i in range(10)) for v in f()))"
   ]
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