MathsJam April 2016 - Reverse Pairs

MathsJam-2016-04_Reverse_Pairs.ipynb

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     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n"
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   ],
   "source": [
    "N = 100\n",
    "ns = list(range(N))\n",
    "print(ns)"
   ]
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     "text": [
      "12 x 42 = 21 x 24\n",
      "12 x 63 = 21 x 36\n",
      "12 x 84 = 21 x 48\n",
      "13 x 62 = 31 x 26\n",
      "13 x 93 = 31 x 39\n",
      "14 x 82 = 41 x 28\n",
      "21 x 24 = 12 x 42\n",
      "21 x 36 = 12 x 63\n",
      "21 x 48 = 12 x 84\n",
      "23 x 64 = 32 x 46\n",
      "23 x 96 = 32 x 69\n",
      "24 x 63 = 42 x 36\n",
      "24 x 84 = 42 x 48\n",
      "26 x 31 = 62 x 13\n",
      "26 x 93 = 62 x 39\n",
      "28 x 41 = 82 x 14\n",
      "31 x 39 = 13 x 93\n",
      "32 x 46 = 23 x 64\n",
      "32 x 69 = 23 x 96\n",
      "34 x 86 = 43 x 68\n",
      "36 x 42 = 63 x 24\n",
      "36 x 84 = 63 x 48\n",
      "39 x 62 = 93 x 26\n",
      "42 x 48 = 24 x 84\n",
      "43 x 68 = 34 x 86\n",
      "46 x 96 = 64 x 69\n",
      "48 x 63 = 84 x 36\n",
      "64 x 69 = 46 x 96\n",
      "Total: 28\n"
     ]
    }
   ],
   "source": [
    "c = 0\n",
    "for i in range(10, N):\n",
    "    for j in range(i + 1, N):\n",
    "        p = ns[i] * ns[j]\n",
    "        ri = int(str(ns[i])[::-1])\n",
    "        rj = int(str(ns[j])[::-1])\n",
    "        r = ri * rj\n",
    "        if p == r and ns[i] != ri and ns[i] != rj:\n",
    "            c += 1\n",
    "            print(ns[i], 'x', ns[j], '=', ri, 'x', rj)\n",
    "print('Total:', c)"
   ]
  }
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