A kōan  is a story, dialogue, question, or statement in the history and lore of Zen Buddhism,  

generally containing aspects that are inaccessible to rational understanding,

yet may be accessible to intuition.

A famous kōan is: "Two hands clap and there is a sound; what is the sound of one hand?"

A student once asked him: "If I haven't anything in my mind, what shall I do?" 

Joshu replied: "Throw it out."

"But if I haven't anything, how can I throw it out?" continued the questioner.

"Well," said Joshu, "then carry it out."

Two monks were watching a flag flapping

in the wind.

One said to the other, "The flag is moving."

The other replied, "The wind is moving."

Huineng overheard this. He said:

"Not the flag, not the wind; mind is moving."

When Bankei was preaching at Ryumon temple, a Shinshu priest, who believed in salvation through repetition of the name of the Buddha of Love,

was jealous of his large audience and wanted to debate with him.

Bankei was in the midst of a talk when the priest appeared, but the fellow made such a disturbance that Bankei stopped his discourse and asked about the noise.

"The founder of our sect," boasted the priest, "had such miraculous powers that he held a brush in his hand on one bank of the river, his attendant held up a paper on the other bank, and the teacher wrote the holy name of Amida through the air.

Can you do such a wonderful thing?"

Bankei replied lightly: "Perhaps your fox can perform that trick, but that is not the manner of Zen. My miracle is that when I feel hungry I eat, and when I feel thirsty I drink."

Joshu began the study of Zen when he was

sixty years old and continued until he was eighty,

when he realized Zen.

He taught from the age of eighty until he was one hundred and twenty.