{"status": "success", "data": {"description_md": "Centered at each lattice point in the coordinate plane are a circle of radius $\\tfrac{1}{10}$ and a square with sides of length $\\tfrac{1}{5}$ whose sides are parallel to the coordinate axes. The line segment from $(0, 0)$ to $(1001, 429)$ intersects $m$ of the squares and $n$ of the circles. Find $m + n$.\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>Centered at each lattice point in the coordinate plane are a circle of radius <span class=\"katex--inline\">\\tfrac{1}{10}</span> and a square with sides of length <span class=\"katex--inline\">\\tfrac{1}{5}</span> whose sides are parallel to the coordinate axes. The line segment from <span class=\"katex--inline\">(0, 0)</span> to <span class=\"katex--inline\">(1001, 429)</span> intersects <span class=\"katex--inline\">m</span> of the squares and <span class=\"katex--inline\">n</span> of the circles. Find <span class=\"katex--inline\">m + n</span>.</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": 6, "problem_name": "2016 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_I_p15", "prev": "/problem/16_aime_I_p13"}}