{"status": "success", "data": {"description_md": "For how many ordered triples $(x,y,z)$ of nonnegative integers less than $20$ are there exactly two distinct elements in the set $\\{i^x, (1+i)^y, z\\}$, where $i=\\sqrt{-1}$?\n\n$\\textbf{(A)}\\ 149 \\qquad \\textbf{(B)}\\ 205 \\qquad \\textbf{(C)}\\ 215 \\qquad \\textbf{(D)}\\ 225 \\qquad \\textbf{(E)}\\ 235$\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>For how many ordered triples  <span class=\"katex--inline\">(x,y,z)</span>  of nonnegative integers less than  <span class=\"katex--inline\">20</span>  are there exactly two distinct elements in the set  <span class=\"katex--inline\">\\{i^x, (1+i)^y, z\\}</span> , where  <span class=\"katex--inline\">i=\\sqrt{-1}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 149 \\qquad \\textbf{(B)}\\ 205 \\qquad \\textbf{(C)}\\ 215 \\qquad \\textbf{(D)}\\ 225 \\qquad \\textbf{(E)}\\ 235</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": "2010 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p16", "prev": "/problem/10_amc12B_p14"}}