{"status": "success", "data": {"description_md": "A small square is constructed inside a square of area 1 by dividing each side of the unit square into $n$ equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of $n$ if the the area of the small square is exactly 1/1985.<br>$\\includegraphics[width=157, height=167, totalheight=167]{https://latex.artofproblemsolving.com/8/6/9/869771a29889569e7f650bf31a1241605514e6bd.png}$\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>A small square is constructed inside a square of area 1 by dividing each side of the unit square into <span class=\"katex--inline\">n</span> equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of <span class=\"katex--inline\">n</span> if the the area of the small square is exactly 1/1985.<br/><img src=\"https://latex.artofproblemsolving.com/8/6/9/869771a29889569e7f650bf31a1241605514e6bd.png\" width=\"157\" height=\"167\" class=\"problem-image\"/></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": "1985 AIME Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p05", "prev": "/problem/85_aime_p03"}}