{"status": "success", "data": {"description_md": "Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersections of the graphs of $$y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))). $$\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>Define <span class=\"katex--inline\">f(x)=|| x|-\\tfrac{1}{2}|</span> and <span class=\"katex--inline\">g(x)=|| x|-\\tfrac{1}{4}|</span>. Find the number of intersections of the graphs of <span class=\"katex--display\">y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).</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": 5, "problem_name": "2024 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p13", "prev": "/problem/24_aime_I_p11"}}