{"status": "success", "data": {"description_md": "A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won $10$ games and lost $10$ games; there were no ties. How many sets of three teams $\\{A, B, C\\}$ were there in which $A$ beat $B$, $B$ beat $C$, and $C$ beat $A?$\n\n$\\textbf{(A)}\\ 385 \\qquad<br>\\textbf{(B)}\\ 665 \\qquad<br>\\textbf{(C)}\\ 945 \\qquad<br>\\textbf{(D)}\\ 1140 \\qquad<br>\\textbf{(E)}\\ 1330$\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>A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won  <span class=\"katex--inline\">10</span>  games and lost  <span class=\"katex--inline\">10</span>  games; there were no ties. How many sets of three teams  <span class=\"katex--inline\">\\{A, B, C\\}</span>  were there in which  <span class=\"katex--inline\">A</span>  beat  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">B</span>  beat  <span class=\"katex--inline\">C</span> , and  <span class=\"katex--inline\">C</span>  beat  <span class=\"katex--inline\">A?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 385 \\qquad\\textbf{(B)}\\ 665 \\qquad\\textbf{(C)}\\ 945 \\qquad\\textbf{(D)}\\ 1140 \\qquad\\textbf{(E)}\\ 1330</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": 3, "problem_name": "2016 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p21", "prev": "/problem/16_amc12B_p19"}}