The fold-and-one-cut problem, often linked to Houdini’s Magic trick, involves making paper cutouts with one straight cut. While the literature leads us to valid crease patterns, it lacks a straightforward teaching method, in particular for the assignment of mountain and valley folds. This paper presents a simplified, pedagogical approach for crafting single- and multi-polygon cutouts, illustrated by examples. Emphasizing origami principles for flat-foldability, our approach transforms the fold-and-one-cut problem into an effective educational tool. Classroom implementation demonstrates the approach’s efficacy in reinforcing student’s understanding of origami design principles. Moreover, our approach promotes hands-on applications of the method, which can be readily implemented beyond the classroom, e.g., workshops and outreach activities.