{"status": "success", "data": {"description_md": "A triangular number is a positive integer that can be expressed in the form $t_n=1+2+3+\\cdots+n$, for some positive integer $n$. The three smallest triangular numbers that are also perfect squares are $t_1=1=1^2, t_8=36=6^2,$ and $t_{49}=1225=35^2$. What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?\n\n$\\textbf{(A)} ~6 \\qquad\\textbf{(B)} ~9 \\qquad\\textbf{(C)} ~12 \\qquad\\textbf{(D)} ~18 \\qquad\\textbf{(E)} ~27$\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 triangular number is a positive integer that can be expressed in the form  <span class=\"katex--inline\">t_n=1+2+3+\\cdots+n</span> , for some positive integer  <span class=\"katex--inline\">n</span> . The three smallest triangular numbers that are also perfect squares are  <span class=\"katex--inline\">t_1=1=1^2, t_8=36=6^2,</span>  and  <span class=\"katex--inline\">t_{49}=1225=35^2</span> . What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} ~6 \\qquad\\textbf{(B)} ~9 \\qquad\\textbf{(C)} ~12 \\qquad\\textbf{(D)} ~18 \\qquad\\textbf{(E)} ~27</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": "2022 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p17", "prev": "/problem/22_amc12A_p15"}}