{"status": "success", "data": {"description_md": "There is a collection of $25$ indistinguishable black chips and $25$ indistinguishable white chips. Find the number of ways to place some of these chips in $25$ unit cells of a $5 \\times 5$ grid so that:<br><br>each cell contains at most one chip,<br>all chips in the same row and all chips in the same column have the same color,<br>any additional chip placed on the grid would violate one or more of the previous two conditions.<br><br>\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>There is a collection of <span class=\"katex--inline\">25</span> indistinguishable black chips and <span class=\"katex--inline\">25</span> indistinguishable white chips. Find the number of ways to place some of these chips in <span class=\"katex--inline\">25</span> unit cells of a <span class=\"katex--inline\">5 \\times 5</span> grid so that:<br/><br/>each cell contains at most one chip,<br/>all chips in the same row and all chips in the same column have the same color,<br/>any additional chip placed on the grid would violate one or more of the previous two conditions.<br/><br/></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": 4, "problem_name": "2024 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_II_p10", "prev": "/problem/24_aime_II_p08"}}