{"status": "success", "data": {"description_md": "For $\\{1, 2, 3, \\ldots, n\\}$ and each of its nonempty subsets a unique alternating sum is defined as follows: Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. (For example, the alternating sum for $\\{1, 2, 4, 6, 9\\}$ is $9 - 6 + 4 - 2 + 1 = 6$ and for $\\{5\\}$ it is simply 5.) Find the sum of all such alternating sums for $n = 7$.\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 <span class=\"katex--inline\">\\{1, 2, 3, \\ldots, n\\}</span> and each of its nonempty subsets a unique alternating sum is defined as follows: Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. (For example, the alternating sum for <span class=\"katex--inline\">\\{1, 2, 4, 6, 9\\}</span> is <span class=\"katex--inline\">9 - 6 + 4 - 2 + 1 = 6</span> and for <span class=\"katex--inline\">\\{5\\}</span> it is simply 5.) Find the sum of all such alternating sums for <span class=\"katex--inline\">n = 7</span>.</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": 6, "problem_name": "1983 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/83_aime_p14", "prev": "/problem/83_aime_p12"}}