{"status": "success", "data": {"description_md": "For some particular value of $N$, when $(a+b+c+d+1)^N$ is expanded and like terms are combined, the resulting expression contains exactly $1001$ terms that include all four variables $a, b,c,$ and $d$, each to some positive power. What is $N$?\n\n$\\textbf{(A) }9 \\qquad \\textbf{(B) } 14 \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19$", "description_html": "<p>For some particular value of  <span class=\"katex--inline\">N</span> , when  <span class=\"katex--inline\">(a+b+c+d+1)^N</span>  is expanded and like terms are combined, the resulting expression contains exactly  <span class=\"katex--inline\">1001</span>  terms that include all four variables  <span class=\"katex--inline\">a, b,c,</span>  and  <span class=\"katex--inline\">d</span> , each to some positive power. What is  <span class=\"katex--inline\">N</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }9 \\qquad \\textbf{(B) } 14 \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19</span> </p>\n<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 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc10A_p21", "prev": "/problem/16_amc10A_p19"}}