{"status": "success", "data": {"description_md": "Bela and Jenn play the following game on the closed interval $[0, n]$ of the real number line, where $n$ is a fixed integer greater than $4$. They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval $[0, n]$. Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?\n\n$\\textbf{(A)} \\text{ Bela will always win.} \\qquad \\textbf{(B)} \\text{ Jenn will always win.} \\qquad \\textbf{(C)} \\text{ Bela will win if and only if }n \\text{ is odd.}$\n\n$\\textbf{(D)} \\text{ Jenn will win if and only if }n \\text{ is odd.} \\qquad \\textbf{(E)} \\text { Jenn will win if and only if } n>8.$\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>Bela and Jenn play the following game on the closed interval  <span class=\"katex--inline\">[0, n]</span>  of the real number line, where  <span class=\"katex--inline\">n</span>  is a fixed integer greater than  <span class=\"katex--inline\">4</span> . They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval  <span class=\"katex--inline\">[0, n]</span> . Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\text{ Bela will always win.} \\qquad \\textbf{(B)} \\text{ Jenn will always win.} \\qquad \\textbf{(C)} \\text{ Bela will win if and only if }n \\text{ is odd.}</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(D)} \\text{ Jenn will win if and only if }n \\text{ is odd.} \\qquad \\textbf{(E)} \\text { Jenn will win if and only if } n&gt;8.</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": "2020 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p15", "prev": "/problem/20_amc12B_p13"}}