{"status": "success", "data": {"description_md": "A total of $n$ points are equally spaced around a circle and are labelled with the integers 1 to $n$, in order. Two points are called *diametrically opposite* if the line segment joining them is a diameter of the circle. If the points labelled 7 and 35 are diametrically opposite, then $n$ equals\n\n$\\text{(A)}\\ 54\\qquad\\text{(B)}\\ 55\\qquad\\text{(C)}\\ 56\\qquad\\text{(D)}\\ 57\\qquad\\text{(E)}\\ 58$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>A total of <span class=\"katex--inline\">n</span> points are equally spaced around a circle and are labelled with the integers 1 to <span class=\"katex--inline\">n</span>, in order. Two points are called *diametrically opposite* if the line segment joining them is a diameter of the circle. If the points labelled 7 and 35 are diametrically opposite, then <span class=\"katex--inline\">n</span> equals</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 54\\qquad\\text{(B)}\\ 55\\qquad\\text{(C)}\\ 56\\qquad\\text{(D)}\\ 57\\qquad\\text{(E)}\\ 58</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2016 Cayley Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/16_cayley_p20", "prev": "/problem/16_cayley_p18"}}