A koan is a paradoxical statement or question used in Zen Buddhism to provoke deep thought and meditation. These often puzzling phrases challenge conventional reasoning and encourage practitioners to transcend logical thinking, leading to a deeper understanding of reality and self. Koans are typically presented by a Zen master to students during meditation practice. The student contemplates the koan, seeking insight and enlightenment. Famous examples include "What is the sound of one hand clapping?" and "If you meet the Buddha on the road, kill him." These serve as tools for spiritual awakening rather than straightforward answers.