{"status": "success", "data": {"description_md": "For a positive integer $n$ and nonzero digits $a$, $b$, and $c$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each of whose digits is equal to $b$, and let $C_n$ be the $2n$-digit (not $n$-digit) integer each of whose digits is equal to $c$. What is the greatest possible value of $a + b + c$ for which there are at least two values of $n$ such that $C_n - B_n = A_n^2$?\n\n$\\textbf{(A) } 12 \\qquad \\textbf{(B) } 14 \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 18 \\qquad \\textbf{(E) } 20$", "description_html": "<p>For a positive integer <span class=\"katex--inline\">n</span> and nonzero digits <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span>, let <span class=\"katex--inline\">A_n</span> be the <span class=\"katex--inline\">n</span>-digit integer each of whose digits is equal to <span class=\"katex--inline\">a</span>; let <span class=\"katex--inline\">B_n</span> be the <span class=\"katex--inline\">n</span>-digit integer each of whose digits is equal to <span class=\"katex--inline\">b</span>, and let <span class=\"katex--inline\">C_n</span> be the <span class=\"katex--inline\">2n</span>-digit (not <span class=\"katex--inline\">n</span>-digit) integer each of whose digits is equal to <span class=\"katex--inline\">c</span>. What is the greatest possible value of <span class=\"katex--inline\">a + b + c</span> for which there are at least two values of <span class=\"katex--inline\">n</span> such that <span class=\"katex--inline\">C_n - B_n = A_n^2</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 12 \\qquad \\textbf{(B) } 14 \\qquad \\textbf{(C) } 16 \\qquad \\textbf{(D) } 18 \\qquad \\textbf{(E) } 20</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2018 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/18_amc10A_p24"}}