project-euler-32-pan-digital-product.ipynb

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    "<p>We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once; for example, the $5$-digit number, $15234$, is $1$ through $5$ pandigital.</p>\n",
    "\n",
    "<p>The product $7254$ is unusual, as the identity, $39 \\times 186 = 7254$, containing multiplicand, multiplier, and product is $1$ through $9$ pandigital.</p>\n",
    "\n",
    "<p>Find the sum of all products whose multiplicand/multiplier/product identity can be written as a $1$ through $9$ pandigital.</p>\n",
    "\n",
    "<div class=\"note\">HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.</div>\n"
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      "4 1738 6952 417386952 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "4 1963 7852 419637852 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "12 483 5796 124835796 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "18 297 5346 182975346 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "27 198 5346 271985346 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "28 157 4396 281574396 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "39 186 7254 391867254 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "42 138 5796 421385796 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "48 159 7632 481597632 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "138 42 5796 138425796 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "157 28 4396 157284396 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "159 48 7632 159487632 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "186 39 7254 186397254 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "198 27 5346 198275346 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "297 18 5346 297185346 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "483 12 5796 483125796 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "1738 4 6952 173846952 {'3', '5', '1', '8', '9', '4', '7', '6', '2'}\n",
      "1963 4 7852 196347852 {'3', '5', '1', '9', '8', '4', '7', '6', '2'}\n",
      "[6952, 7852, 5796, 5346, 5346, 4396, 7254, 5796, 7632, 5796, 4396, 7632, 7254, 5346, 5346, 5796, 6952, 7852]\n",
      "The total sum of pan digital is 45228\n"
     ]
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   "source": [
    "def has_repeating_number(number):\n",
    "    num_str = str(number)\n",
    "    return len(num_str) != len(set(num_str))\n",
    "\n",
    "def is_pan_digit(multiplicand, multiplier, product):\n",
    "    combined = str(multiplicand) + str(multiplier) + str(product)\n",
    "    return len(combined) == 9 and set(combined) == set(\"123456789\")\n",
    "    \n",
    "pan_sum = []\n",
    "for i in range(4,5000):\n",
    "    if has_repeating_number(i):\n",
    "        continue\n",
    "    # print(i)\n",
    "    for j in range(1,100000):\n",
    "        if has_repeating_number(j):\n",
    "            continue\n",
    "        product = i * j \n",
    "        # if has_repeating_number(product):\n",
    "        #     continue\n",
    "        # if is_pan_digit(i,j,product):\n",
    "        pan_num = str(i) + str(j) + str(product)\n",
    "        if len(pan_num) > 9:\n",
    "            break\n",
    "        if has_repeating_number(int(pan_num))==False and is_pan_digit(i,j,product):\n",
    "            print(i,j,product, pan_num, set(pan_num))\n",
    "            pan_sum.append(product)\n",
    "print(pan_sum)        \n",
    "print(f\"The total sum of pan digital is {sum(set(pan_sum))}\")"
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