<p>Let <img alt="$S$" height="14" src="https://latex.artofproblemsolving.com/a/d/2/ad28c83c99a8fd0dd2e2e594c9d02ee532765a0a.png" width="14" /> be the set of vertices of a regular <img alt="$24$" height="12" src="https://latex.artofproblemsolving.com/e/2/9/e290f2cba0ba0e11c0b91630da15a408da2fcf1c.png" width="18" />-gon. Find the number of ways to draw <img alt="$12$" height="12" src="https://latex.artofproblemsolving.com/e/d/f/edf074831eb5bc9e61d6d6e09f525a86e3068f6a.png" width="17" /> segments of equal lengths so that each vertex in <img alt="$S$" height="14" src="https://latex.artofproblemsolving.com/a/d/2/ad28c83c99a8fd0dd2e2e594c9d02ee532765a0a.png" width="14" /> is an endpoint of exactly one of the <img alt="$12$" height="12" src="https://latex.artofproblemsolving.com/e/d/f/edf074831eb5bc9e61d6d6e09f525a86e3068f6a.png" width="17" /> segments.</p>

Question No: 334

Let $S$ be the set of vertices of a regular $24$ -gon. Find the number of ways to draw $12$ segments of equal lengths so that each vertex in $S$ is an endpoint of exactly one of the $12$ segments.

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Tags: Combinatorics Geometry

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