A koan is a Buddhist meditation tool-- it's a nonsense question that one meditates on an answer for, but since its nonsense in terms of logic, they have to come up with a creative symbolic answer. The most famous one is "what is the sound of one hand clapping?" Disciples would present their answers to the master, and he would decide if they need to consider it longer or move on to a new one.

Love your writing, thanks for engaging! :)