{"status": "success", "data": {"description_md": "A drawer contains a mixture of red socks and blue socks, at most 1991 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly $1/2$ that both are red or both are blue. What is the largest possible number of red socks in the drawer that is consistent with this data?\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>A drawer contains a mixture of red socks and blue socks, at most 1991 in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly <span class=\"katex--inline\">1/2</span> that both are red or both are blue. What is the largest possible number of red socks in the drawer that is consistent with this data?</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": "1991 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/91_aime_p14", "prev": "/problem/91_aime_p12"}}