In the Second Scroll of Wen the Eternally Surprised, a story is written
concerning one day when the apprentice Clodpool, in a rebellious
mood, approached Wen and spake thusly:
“Master, what is the difference between a humanistic, monastic
system of belief in which wisdom in sought by means of an
apparently nonsensical system of questions and answers, and a lot
of mystic gibberish made up on the spur of the moment?”
Wen considered this for some time, and at last said: “A fish!”
Once the monks of the Western and Eastern Halls were arguing about a cat. Nansen, holding up the cat, said, “You monks! If you can say a word of Zen, I will spare the cat. Otherwise I will kill it.” No one could answer, so Nansen cut the cat in two. That evening, when Joshu returned, Nansen told him of the incident. Joshu thereupon took off his sandal, put it on his head, and walked off. Nansen said, “If you had been there, the cat would have been saved!”
I love how, even never having read this before, I know it’s Terry Pratchett
Here’s a legit Zen koan that fits the bill:
Mumonkan number 14: Nansen kills the cat
Once the monks of the Western and Eastern Halls were arguing about a cat. Nansen, holding up the cat, said, “You monks! If you can say a word of Zen, I will spare the cat. Otherwise I will kill it.” No one could answer, so Nansen cut the cat in two. That evening, when Joshu returned, Nansen told him of the incident. Joshu thereupon took off his sandal, put it on his head, and walked off. Nansen said, “If you had been there, the cat would have been saved!”