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How did Hakuin use the sound of one hand clapping as a Zen koan?

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The Japanese priest Hakuin is credited with inventing the famous koan, "When both hands are clapped a sound is produced; listen to the sound of one hand clapping."12

In the context of Rinzai Zen Buddhism, Hakuin utilized this paradox as a meditation discipline to aid his students. The primary purpose of such a koan is to exhaust the student's analytic intellect and egoistic will. By presenting an unsolvable riddle, Hakuin intended to force the mind beyond logical reasoning, preparing the novice to experience an intuitive response and attain enlightenment.12