Euler 040 - Champernowne's constant.ipynb

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    "Euler Problem 40\n",
    "================\n",
    "\n",
    "An irrational decimal fraction is created by concatenating the positive integers:\n",
    "\n",
    "    0.123456789101112131415161718192021...\n",
    "\n",
    "It can be seen that the 12th digit of the fractional part is 1.\n",
    "\n",
    "If $d_n$ represents the nth digit of the fractional part, find the value of the following expression.\n",
    "\n",
    "$$d_1 \\times d_{10} \\times d_{100} \\times d_{1000} \\times d_{10000} \\times d_{100000} \\times d_{1000000}$$"
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      "210\n"
     ]
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   "source": [
    "def champernowne_digit(n):\n",
    "    digits = 1\n",
    "    power = 1\n",
    "    while n > 9 * digits * power:\n",
    "        n -= 9 * digits * power\n",
    "        digits += 1\n",
    "        power *= 10\n",
    "    return int(str(power + (n-1) // digits)[(n-1) % digits])\n",
    "\n",
    "from functools import reduce\n",
    "print(reduce(lambda x,y: x*y, (champernowne_digit(10**k) for k in range(7))))"
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