A koan is not a riddle to be solved. It is a phrase designed to resist conceptual resolution — what is the sound of one hand clapping?, show me your original face before your parents were born, or the classic mu (the master’s answer to “does a dog have buddha-nature?” — nothing/not).
The student sits with the koan, often for weeks or years, until thinking is exhausted. What arrives is not an answer but a direct seeing that renders the question dissolved. This is the rinzai Zen method most explicitly; Soto Zen emphasizes Zazen without koan.