{"status": "success", "data": {"description_md": "Let $S$ be the square one of whose diagonals has endpoints $(0.1,0.7)$ and $(-0.1,-0.7)$. A point $v=(x,y)$ is chosen uniformly at random over all pairs of real numbers $x$ and $y$ such that $0 \\le x \\le 2012$ and $0\\le y\\le 2012$. Let $T(v)$ be a translated copy of $S$ centered at $v$. What is the probability that the square region determined by $T(v)$ contains exactly two points with integer coordinates in its interior?\n\n$\\textbf{(A)}\\ \\frac{1}{8}\\qquad\\textbf{(B) }\\frac{7}{50}\\qquad\\textbf{(C) }\\frac{4}{25}\\qquad\\textbf{(D) }\\frac{1}{4}\\qquad\\textbf{(E) }\\frac{8}{25}$\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": "

Let S be the square one of whose diagonals has endpoints (0.1,0.7) and (-0.1,-0.7) . A point v=(x,y) is chosen uniformly at random over all pairs of real numbers x and y such that 0 \\le x \\le 2012 and 0\\le y\\le 2012 . Let T(v) be a translated copy of S centered at v . What is the probability that the square region determined by T(v) contains exactly two points with integer coordinates in its interior?

\\textbf{(A)}\\ \\frac{1}{8}\\qquad\\textbf{(B) }\\frac{7}{50}\\qquad\\textbf{(C) }\\frac{4}{25}\\qquad\\textbf{(D) }\\frac{1}{4}\\qquad\\textbf{(E) }\\frac{8}{25}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2012 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p24", "prev": "/problem/12_amc12A_p22"}}