{"status": "success", "data": {"description_md": "For $t = 1, 2, 3, 4$, define $\\displaystyle S_t = \\sum_{i = 1}^{350}a_i^t$, where $a_i \\in \\{1,2,3,4\\}$. If $S_1 = 513$ and $S_4 = 4745$, find the minimum possible value for $S_2$.\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\">t = 1, 2, 3, 4</span>, define <span class=\"katex--inline\">\\displaystyle S_t = \\sum_{i = 1}^{350}a_i^t</span>, where <span class=\"katex--inline\">a_i \\in \\{1,2,3,4\\}</span>. If <span class=\"katex--inline\">S_1 = 513</span> and <span class=\"katex--inline\">S_4 = 4745</span>, find the minimum possible value for <span class=\"katex--inline\">S_2</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2009 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_I_p15", "prev": "/problem/09_aime_I_p13"}}