{"status": "success", "data": {"description_md": "A frog begins at $P_0 = (0,0)$ and makes a sequence of jumps according to the following rule: from $P_n=(x_n,y_n)$, the frog jumps to $P_{n+1}$, which may be any of the points $(x_n+7, y_n+2)$, $(x_n+2,y_n+7)$, $(x_n-5, y_n-10)$, or $(x_n-10,y_n-5)$. There are $M$ points $(x,y)$ with $|x|+|y| \\le 100$ that can be reached by a sequence of such jumps. Find the remainder when $M$ 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>A frog begins at <span class=\"katex--inline\">P_0 = (0,0)</span> and makes a sequence of jumps according to the following rule: from <span class=\"katex--inline\">P_n=(x_n,y_n)</span>, the frog jumps to <span class=\"katex--inline\">P_{n+1}</span>, which may be any of the points <span class=\"katex--inline\">(x_n+7, y_n+2)</span>, <span class=\"katex--inline\">(x_n+2,y_n+7)</span>, <span class=\"katex--inline\">(x_n-5, y_n-10)</span>, or <span class=\"katex--inline\">(x_n-10,y_n-5)</span>. There are <span class=\"katex--inline\">M</span> points <span class=\"katex--inline\">(x,y)</span> with <span class=\"katex--inline\">|x|+|y| \\le 100</span> that can be reached by a sequence of such jumps. Find the remainder when <span class=\"katex--inline\">M</span> is divided by <span class=\"katex--inline\">1000</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": 5, "problem_name": "2012 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_I_p12", "prev": "/problem/12_aime_I_p10"}}