{"status": "success", "data": {"description_md": "Let $S$ be the set of all points with coordinates $(x,y,z)$, where $x, y,$ and $z$ are each chosen from the set $\\{ 0, 1, 2\\}$. How many equilateral triangles have all their vertices in $S$?\n\n$\\mathrm {(A) } 72 \\qquad \\mathrm {(B) } 76 \\qquad \\mathrm {(C) } 80 \\qquad \\mathrm {(D) } 84 \\qquad \\mathrm {(E) } 88$\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>Let  <span class=\"katex--inline\">S</span>  be the set of all points with coordinates  <span class=\"katex--inline\">(x,y,z)</span> , where  <span class=\"katex--inline\">x, y,</span>  and  <span class=\"katex--inline\">z</span>  are each chosen from the set  <span class=\"katex--inline\">\\{ 0, 1, 2\\}</span> . How many equilateral triangles have all their vertices in  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A) } 72 \\qquad \\mathrm {(B) } 76 \\qquad \\mathrm {(C) } 80 \\qquad \\mathrm {(D) } 84 \\qquad \\mathrm {(E) } 88</span> </p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2005 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/05_amc12A_p24"}}