{"status": "success", "data": {"description_md": "The numbers $1,2,\\ldots,9$ are randomly placed into the $9$ squares of a $3 \\times 3$ grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row and each column is odd?\n\n$\\textbf{(A) }\\frac{1}{21}\\qquad\\textbf{(B) }\\frac{1}{14}\\qquad\\textbf{(C) }\\frac{5}{63}\\qquad\\textbf{(D) }\\frac{2}{21}\\qquad\\textbf{(E) } \\frac17$\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>The numbers  <span class=\"katex--inline\">1,2,\\ldots,9</span>  are randomly placed into the  <span class=\"katex--inline\">9</span>  squares of a  <span class=\"katex--inline\">3 \\times 3</span>  grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row and each column is odd?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }\\frac{1}{21}\\qquad\\textbf{(B) }\\frac{1}{14}\\qquad\\textbf{(C) }\\frac{5}{63}\\qquad\\textbf{(D) }\\frac{2}{21}\\qquad\\textbf{(E) } \\frac17</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": "2019 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p17", "prev": "/problem/19_amc12A_p15"}}