{"status": "success", "data": {"description_md": "Let $\\mathcal{S}$ be the set of all perfect squares whose rightmost three digits in base $10$ are $256$. Let $\\mathcal{T}$ be the set of all numbers of the form $\\frac{x-256}{1000}$, where $x$ is in $\\mathcal{S}$. In other words, $\\mathcal{T}$ is the set of numbers that result when the last three digits of each number in $\\mathcal{S}$ are truncated. Find the remainder when the tenth smallest element of $\\mathcal{T}$ 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>Let <span class=\"katex--inline\">\\mathcal{S}</span> be the set of all perfect squares whose rightmost three digits in base <span class=\"katex--inline\">10</span> are <span class=\"katex--inline\">256</span>. Let <span class=\"katex--inline\">\\mathcal{T}</span> be the set of all numbers of the form <span class=\"katex--inline\">\\frac{x-256}{1000}</span>, where <span class=\"katex--inline\">x</span> is in <span class=\"katex--inline\">\\mathcal{S}</span>. In other words, <span class=\"katex--inline\">\\mathcal{T}</span> is the set of numbers that result when the last three digits of each number in <span class=\"katex--inline\">\\mathcal{S}</span> are truncated. Find the remainder when the tenth smallest element of <span class=\"katex--inline\">\\mathcal{T}</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 10", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_I_p11", "prev": "/problem/12_aime_I_p09"}}