Hakuin Ekaku (1686-1769), "What is the sound of one hand clapping?" is the best-known koan devised by a Japanese master.
Like all Zen methods, the Koan is a way to practice meditation. Meditation focusing on the Koan is a path. The purpose of a Koan is to create doubt in the conscious mind because the Koan does not have one logical, reasoned answer. The Koan is like an onion that you peal back to find infinite layers of answers. The practice of repetition to find a deeper answer to a Koan increases doubt and leads to the Great Doubt.
On the path one answer to the Koan: Nothing. As a metaphor, one hand becomes one person. An individual taking action results in no sound other than the individual action. We are nothing without others. Our thoughts continue along this path of increasing doubt that we have one logical and reasoned answer.
In Zen the word Mu means nothing. Using logic and reason, we use words to describe what is happening in the conscious mind. Mu means without logic or reason, without using our conscious mind. Zen is the art of always going deeper into our subconscious.
We have two parts to our brain. The art of mediation is to probe the conscious mind to find connects with the ancient part of our brain that does not use logic or reason, words or numbers.