40.ipynb

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   "source": [
    "# Champernowne's Constant"
   ]
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   "source": [
    "## Problem 40"
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    "An irrational decimal fraction is created by concatenating the positive integers:\n",
    "<center>0.123456789101112131415161718192021...</center>\n",
    "It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.\n",
    "If $d_{n}$ represents the n<sup>th</sup> digit of the fractional part, find the value of the following expression.\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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    "# Create irrational decimal fraction; omit \"0.\" at the beginning\n",
    "irrational_fract = \".\"\n",
    "n = 1\n",
    "len_max = 1000000 + 1\n",
    "\n",
    "# Build up the irrational fraction string up to len_max\n",
    "while len(irrational_fract) < len_max:\n",
    "    irrational_fract += str(n)\n",
    "    n += 1"
   ]
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    "# Collect digits at positions 1, 10, 100, ... up to 1,000,000\n",
    "d_s = []\n",
    "d = 1\n",
    "while d < len_max:\n",
    "    d_n = int(irrational_fract[d])  # Accessing within bounds\n",
    "    d_s.append(d_n)\n",
    "    d *= 10"
   ]
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     "text": [
      "210\n"
     ]
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   "source": [
    "# Print the result\n",
    "import math\n",
    "d_n_product = math.prod(i for i in d_s)\n",
    "print(d_n_product)"
   ]
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