finding_operators.ipynb

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   "source": [
    "import itertools"
   ]
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    "questions = [\n",
    "    (1, '4433', 6),\n",
    "    (2, '8699', 19),\n",
    "    (3, '8978', 20),\n",
    "    (4, '8173', 58),\n",
    "    (5, '3459', 50),\n",
    "    (6, '3528', 17),\n",
    "    (7, '7378', 135),\n",
    "    (8, '3766', 587),\n",
    "    (9, '4245', 471),\n",
    "    (10, '2783', 844),\n",
    "    (11, '7856', 535),\n",
    "    (12, '1395', 80),\n",
    "    (13, '4549', 96)\n",
    "]"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
     "name": "stdout",
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     "text": [
      " >> (((4-4)+3)+3) = 6, ('-', '+', '+')\n",
      "1: 15 ways to solve.\n",
      " >> (((9-6)*9)-8) = 19, ('-', '*', '-')\n",
      "2: 1 ways to solve.\n",
      "3: 0 ways to solve.\n",
      " >> (((8*7)-1)+3) = 58, ('*', '-', '+')\n",
      "4: 4 ways to solve.\n",
      " >> (((4**3)-5)-9) = 50, ('**', '-', '-')\n",
      "5: 6 ways to solve.\n",
      " >> (((3+2)*5)-8) = 17, ('+', '*', '-')\n",
      "6: 17 ways to solve.\n",
      "7: 0 ways to solve.\n",
      "8: 0 ways to solve.\n",
      "9: 0 ways to solve.\n",
      "10: 0 ways to solve.\n",
      "11: 0 ways to solve.\n",
      "12: 0 ways to solve.\n",
      "13: 0 ways to solve.\n"
     ]
    }
   ],
   "source": [
    "# operators_perm = list(itertools.permutations(['+', '-', '*', '/'], 3))\n",
    "# duplicable\n",
    "operators_perm = list(itertools.product(['+', '-', '*', '/', '**'], repeat=3))\n",
    "\n",
    "# loop through all questions\n",
    "for n, q, ans in questions:\n",
    "    # a flag for 'first answer is found'\n",
    "    got_for_n = False\n",
    "    # a list to store solved question string to get unique questions\n",
    "    solver = []\n",
    "    # loop through permutations of question\n",
    "    for qp in itertools.permutations(list(q)):\n",
    "        # temp string with {} to format in operators later\n",
    "        s = '{}'.join(qp)\n",
    "        # add parentheses for correct order of calculation\n",
    "        with_oprt_space = '((({}){}){})'.format(s[:4], s[4:7], s[7:])\n",
    "        # loop through permutations of operators defined above\n",
    "        for oprt in operators_perm:\n",
    "            # construct a question to test (add operators into question)\n",
    "            test_question = with_oprt_space.format(oprt[0], oprt[1], oprt[2])\n",
    "            # if result of test question matches with answer\n",
    "            if eval(test_question) == ans:\n",
    "                if not got_for_n:\n",
    "                    # print if this is the first answer\n",
    "                    print(' >> {} = {}, {}'.format(test_question, ans, oprt))\n",
    "                    # set this flag to True to avoid printing again\n",
    "                    # (only print once for each question)\n",
    "                    got_for_n = True\n",
    "                # also collect question in a list to get uniques later\n",
    "                solver.append(test_question)\n",
    "    # get unique way of current loop question\n",
    "    ways = list(set(solver))\n",
    "    # print how many ways this question can be solved\n",
    "    print(\"{}: {} ways to solve.\".format(n, len(ways)))"
   ]
  }
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