2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138428The Horizontal Chord Theorem states that if a continuous curve connects points $A$ and $B$ in the plane, then for any integer $k$ there are points $C$ and $D$ on the curve such that $\overrightarrow{AB}=k \overrightarrow{CD}$. In this note, we discuss a few combinatorial-analysis problems related to this theorem and introduce a different formulation that gives way to generalizations on graphs.10 pagesGroup Theory05C40, 05C45, 05C75text