{"status": "success", "data": {"description_md": "Let $S$ be the set of all rational numbers $r$, $0<r<1$, that have a repeating decimal expansion in the form $$0.abcabcabc\\ldots=0.\\overline{abc}, $$where the digits $a$, $b$, and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numerators are required?\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\">S</span> be the set of all rational numbers <span class=\"katex--inline\">r</span>, <span class=\"katex--inline\">0&lt;r&lt;1</span>, that have a repeating decimal expansion in the form <span class=\"katex--display\">0.abcabcabc\\ldots=0.\\overline{abc},</span>where the digits <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are not necessarily distinct. To write the elements of <span class=\"katex--inline\">S</span> as fractions in lowest terms, how many different numerators are required?</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": "1992 AIME Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/92_aime_p06", "prev": "/problem/92_aime_p04"}}