{"status": "success", "data": {"description_md": "Define a T-grid to be a $ 3\\times3$ matrix which satisfies the following two properties:<br><br>(1) Exactly five of the entries are $ 1$'s, and the remaining four entries are $ 0$'s.<br>(2) Among the eight rows, columns, and long diagonals (the long diagonals are $ \\{a_{13},a_{22},a_{31}\\}$ and $ \\{a_{11},a_{22},a_{33}\\}$, no more than one of the eight has all three entries equal.<br><br>Find the number of distinct T-grids.\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 a T-grid to be a $ 3\\times3$ matrix which satisfies the following two properties:<br/><br/>(1) Exactly five of the entries are $ 1$'s, and the remaining four entries are $ 0$'s.<br/>(2) Among the eight rows, columns, and long diagonals (the long diagonals are $ {a_{13},a_{22},a_{31}}$ and $ {a_{11},a_{22},a_{33}}$, no more than one of the eight has all three entries equal.<br/><br/>Find the number of distinct T-grids.</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": "2010 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p12", "prev": "/problem/10_aime_II_p10"}}