{"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$\\textbf{(A) }\\dfrac{1}{21}\\qquad\\textbf{(B) }\\dfrac{1}{14}\\qquad\\textbf{(C) }\\dfrac{5}{63}\\qquad\\textbf{(D) }\\dfrac{2}{21}\\qquad\\textbf{(E) }\\dfrac{1}{7}$", "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) }\\dfrac{1}{21}\\qquad\\textbf{(B) }\\dfrac{1}{14}\\qquad\\textbf{(C) }\\dfrac{5}{63}\\qquad\\textbf{(D) }\\dfrac{2}{21}\\qquad\\textbf{(E) }\\dfrac{1}{7}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2019 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10A_p21", "prev": "/problem/19_amc10A_p19"}}