{"status": "success", "data": {"description_md": "Call a set of integers ''spacy'' if it contains no more than one out of any three consecutive integers. How many subsets of $\\{1,2,3,\\ldots,12\\},$ including the empty set, are spacy?<br>\t\n\n$\\mathrm{(A)}\\ 121 \\qquad \\mathrm{(B)}\\ 123 \\qquad \\mathrm{(C)}\\ 125 \\qquad \\mathrm{(D)}\\ 127 \\qquad \\mathrm{(E)}\\ 129$\n___\nFull 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>Call a set of integers &#8216;&#8216;spacy&#8217;&#8217; if it contains no more than one out of any three consecutive integers. How many subsets of <span class=\"katex--inline\">\\{1,2,3,\\ldots,12\\},</span> including the empty set, are spacy?<br/></p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 121 \\qquad \\mathrm{(B)}\\ 123 \\qquad \\mathrm{(C)}\\ 125 \\qquad \\mathrm{(D)}\\ 127 \\qquad \\mathrm{(E)}\\ 129</span></p>&#10;<hr/>&#10;<p>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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2007 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/07_amc12A_p24"}}