{"status": "success", "data": {"description_md": "Let $S$ be a subset of $\\{1,2,3,\\ldots,1989\\}$ such that no two members of $S$ differ by $4$ or $7$. What is the largest number of elements $S$ can have?\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>Let <span class=\"katex--inline\">S</span> be a subset of <span class=\"katex--inline\">\\{1,2,3,\\ldots,1989\\}</span> such that no two members of <span class=\"katex--inline\">S</span> differ by <span class=\"katex--inline\">4</span> or <span class=\"katex--inline\">7</span>. What is the largest number of elements <span class=\"katex--inline\">S</span> can have?</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": "1989 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p14", "prev": "/problem/89_aime_p12"}}