061-cyclical-figurate-numbers.ipynb

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    "# Cyclical figurate numbers\n",
    "## Problem 61 \n",
    "\n",
    "<div class=\"problem_content\" role=\"problem\">\n",
    "<p>Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:</p>\n",
    "<table><tr><td>Triangle</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>3,<i>n</i></sub>=<i>n</i>(<i>n</i>+1)/2</td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 3, 6, 10, 15, ...</td>\n",
    "</tr><tr><td>Square</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>4,<i>n</i></sub>=<i>n</i><sup>2</sup></td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 4, 9, 16, 25, ...</td>\n",
    "</tr><tr><td>Pentagonal</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>5,<i>n</i></sub>=<i>n</i>(3<i>n</i>&#8722;1)/2</td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 5, 12, 22, 35, ...</td>\n",
    "</tr><tr><td>Hexagonal</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>6,<i>n</i></sub>=<i>n</i>(2<i>n</i>&#8722;1)</td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 6, 15, 28, 45, ...</td>\n",
    "</tr><tr><td>Heptagonal</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>7,<i>n</i></sub>=<i>n</i>(5<i>n</i>&#8722;3)/2</td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 7, 18, 34, 55, ...</td>\n",
    "</tr><tr><td>Octagonal</td>\n",
    "<td>&#160;</td>\n",
    "<td>P<sub>8,<i>n</i></sub>=<i>n</i>(3<i>n</i>&#8722;2)</td>\n",
    "<td>&#160;</td>\n",
    "<td>1, 8, 21, 40, 65, ...</td>\n",
    "</tr></table><p>The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.</p>\n",
    "<ol><li>The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).</li>\n",
    "<li>Each polygonal type: triangle (P<sub>3,127</sub>=8128), square (P<sub>4,91</sub>=8281), and pentagonal (P<sub>5,44</sub>=2882), is represented by a different number in the set.</li>\n",
    "<li>This is the only set of 4-digit numbers with this property.</li>\n",
    "</ol><p>Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.</p>\n",
    "</div>"
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   "source": [
    "def solve():\n",
    "    # Your code here\n",
    "    \n"
   ]
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   "source": [
    "## Solution"
   ]
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   "execution_count": null,
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   "outputs": [],
   "source": [
    "solve()"
   ]
  }
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