{"status": "success", "data": {"description_md": "In a $6\\times4$ grid, $12$ of the $24$ squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let $N$ be the number of shadings with this property. Find the remainder when $N$ is divided by $1000$.\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>In a <span class=\"katex--inline\">6\\times4</span> grid, <span class=\"katex--inline\">12</span> of the <span class=\"katex--inline\">24</span> squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let <span class=\"katex--inline\">N</span> be the number of shadings with this property. Find the remainder when <span class=\"katex--inline\">N</span> is divided by <span class=\"katex--inline\">1000</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": 5, "problem_name": "2007 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/07_aime_I_p11", "prev": "/problem/07_aime_I_p09"}}