036-Solution.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# The decimal number, 585 = $1001001001_{2}$ (binary), is palindromic in both bases.\n",
    "\n",
    "# Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.\n",
    "\n",
    "# (Please note that the palindromic number, in either base, may not include leading zeros.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_____\n",
    "\n",
    "# First, finding palindromic decimal numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_palindromic(n):\n",
    "    list_version = list(str(n))\n",
    "    if list_version == list_version[::-1]:\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "list_candidates = [x for x in range(1,1000000) if check_palindromic(x)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now, checking the binary version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "list_results = [x for x in list_candidates if check_palindromic(bin(x)[2:])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 9,\n",
       " 33,\n",
       " 99,\n",
       " 313,\n",
       " 585,\n",
       " 717,\n",
       " 7447,\n",
       " 9009,\n",
       " 15351,\n",
       " 32223,\n",
       " 39993,\n",
       " 53235,\n",
       " 53835,\n",
       " 73737,\n",
       " 585585]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "872187"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(list_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Answer: 872,187"
   ]
  }
 ],
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