{"status": "success", "data": {"description_md": "$\\angle BAC$ is said to be \"laceable\" if distinct points $X_1, X_2, \\ldots, X_{2n}$ can be found so that\n\n- $X_{2k-1}$ is on $AC$ for each value of $k$,\n- $X_{2k}$ is on $AB$ for each value of $k$, and\n- $AX_1 = X_1X_2 = X_2X_3 = \\cdots = X_{2n-1}X_{2n} = X_{2n}A$.\n\nFor example, the angle $20^\\circ$ is laceable, as shown. The number of laceable acute angles, whose sizes in degrees are integers, is\n\n
\"figure\"
\n\n$\\text{(A)}\\ 3\\qquad\\text{(B)}\\ 4\\qquad\\text{(C)}\\ 5\\qquad\\text{(D)}\\ 6\\qquad\\text{(E)}\\ 7$\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": "

\\angle BAC is said to be \"laceable\" if distinct points X_1, X_2, \\ldots, X_{2n} can be found so that

\n

- X_{2k-1} is on AC for each value of k,\n- X_{2k} is on AB for each value of k, and\n- AX_1 = X_1X_2 = X_2X_3 = \\cdots = X_{2n-1}X_{2n} = X_{2n}A.

\n

For example, the angle 20^\\circ is laceable, as shown. The number of laceable acute angles, whose sizes in degrees are integers, is

\n
\"figure\"
\n

\\text{(A)}\\ 3\\qquad\\text{(B)}\\ 4\\qquad\\text{(C)}\\ 5\\qquad\\text{(D)}\\ 6\\qquad\\text{(E)}\\ 7

\n
\n

Cayley, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 Cayley Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/03_cayley_p24"}}