{"status": "success", "data": {"description_md": "An $a\\times b\\times c$ rectangular box is built from $a\\cdot b \\cdot c$ unit cubes. Each unit cube is colored red, green, or yellow. Each of the $a$ layers of size $1\\times b \\times c$ parallel to the $(b\\times c)$-faces of the box contains exactly $9$ red cubes, exactly 12 green cubes, and some yellow cubes. Each of the $b$ layers of size $a\\times 1 \\times c$ parallel to the $(a\\times c)$-faces of the box contains exactly 20 green cubes, exactly 25 yellow cubes, and some red cubes. Find the smallest possible volume of the box.\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>An <span class=\"katex--inline\">a\\times b\\times c</span> rectangular box is built from <span class=\"katex--inline\">a\\cdot b \\cdot c</span> unit cubes. Each unit cube is colored red, green, or yellow. Each of the <span class=\"katex--inline\">a</span> layers of size <span class=\"katex--inline\">1\\times b \\times c</span> parallel to the <span class=\"katex--inline\">(b\\times c)</span>-faces of the box contains exactly <span class=\"katex--inline\">9</span> red cubes, exactly 12 green cubes, and some yellow cubes. Each of the <span class=\"katex--inline\">b</span> layers of size <span class=\"katex--inline\">a\\times 1 \\times c</span> parallel to the <span class=\"katex--inline\">(a\\times c)</span>-faces of the box contains exactly 20 green cubes, exactly 25 yellow cubes, and some red cubes. Find the smallest possible volume of the box.</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": 3, "problem_name": "2016 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p05", "prev": "/problem/16_aime_II_p03"}}