{"status": "success", "data": {"description_md": "For each permutation $ a_1, a_2, a_3, \\ldots,a_{10}$ of the integers $ 1,2,3,\\ldots,10,$ form the sum<br>\n$$ |a_1 - a_2| + |a_3 - a_4| + |a_5 - a_6| + |a_7 - a_8| + |a_9 - a_{10}|. $$ The average value of all such sums can be written in the form $ p/q,$ where $ p$ and $ q$ are relatively prime positive integers. Find $ p + q.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For each permutation $ a_1, a_2, a_3, \\ldots,a_{10}$ of the integers $ 1,2,3,\\ldots,10,$ form the sum<br/><span class=\"katex--display\"> |a_1 - a_2| + |a_3 - a_4| + |a_5 - a_6| + |a_7 - a_8| + |a_9 - a_{10}|.</span><br/>The average value of all such sums can be written in the form $ p/q,$ where $ p$ and $ q$ are relatively prime positive integers. Find $ p + q.$</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "1996 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/96_aime_p13", "prev": "/problem/96_aime_p11"}}