You can lead a horse to water...and if it does the backstroke you have something.
Some time ago I read the Tao of Pooh, the Tao of Peanuts. and the Dancing Wu Li Masters. These books challenged my logic, which was linear and loaded with expectations of knowing in order to gain a deep understanding which would thereby make my life perfect...life is what happens while we are planning our future.
By way of general definition, a Chan or Zen koan is a an opportunity to crash and burn and become a Phoenix. Each is a teacher's crafted set of words (skillful means) into which a student can deep-dive into self, awareness, knowing, and not-knowing. The term translates as "public address, statement or case." The Chan koans sprouted in the Tang and Song Dynasties in China (618-1279 CE). These were skillful constructs as gates to a new dimension of awareness. They were made to be carried gently throughout days of incubation. One eats, drinks and sleeps within the koan. And it is in this relationship that awareness shifts.
This shifting awareness makes big small, white black, and few many-things are not what they seem. Koans are "round, and rolly, slippery, and slick," until they are not. How you might ask? Well, we play and dance. Playing is exploring and dancing is flexing. So what do we explore and how are we flexible.
We explore the koan through the Dharma as Buddha's teachings, mainly the Three Laws, Four Noble Truths, and Noble EightFold Path. What is the koan saying about the great meaning of birth and death? And, in this process we misstep, retrace old steps and jump into new foot-placements, while laughing and getting frustrated.
The Old Woman stood at the Dharma Gate of each seeker, but they only imagined a mountain...