{"status": "success", "data": {"description_md": "In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements.<br>Brian: \"Mike and I are different species.\"<br>Chris: \"LeRoy is a frog.\"<br>LeRoy: \"Chris is a frog.\"<br>Mike: \"Of the four of us, at least two are toads.\"<br>How many of these amphibians are frogs?\n\n$\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 1 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ 3 \\qquad \\textbf{(E)}\\ 4$\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>In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements.<br/>Brian: &#34;Mike and I are different species.&#34;<br/>Chris: &#34;LeRoy is a frog.&#34;<br/>LeRoy: &#34;Chris is a frog.&#34;<br/>Mike: &#34;Of the four of us, at least two are toads.&#34;<br/>How many of these amphibians are frogs?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 1 \\qquad \\textbf{(C)}\\ 2 \\qquad \\textbf{(D)}\\ 3 \\qquad \\textbf{(E)}\\ 4</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": 3, "problem_name": "2010 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p13", "prev": "/problem/10_amc12A_p11"}}