4 ideas
A professor visits Nan-in to learn about Zen, and Nan-in keeps pouring tea until the cup overflows, then says the professor is like this cup, too full of his own opinions to receive anything. The mechanism is that existing conclusions take up the room a new understanding would need, so learning begins with emptying rather than adding.
Tanzan carries a young woman across a muddy road, and hours later his companion Ekido angrily says monks should not go near women. Tanzan replies that he set her down back there and asks why Ekido is still carrying her. The rule-follower who avoided the act holds onto it far longer than the person who did it and let it go, so the mental burden lies in the rumination, not the deed.
Gateless Gate koans such as Joshu's 'Mu' are built so that no conceptual answer settles them, which pushes the student to keep up an intense doubt until discursive thinking gives out. Insight comes when the questioner stops treating the question as a puzzle to solve and understands it directly. The 'gate' has no gate: the barrier is the habit of reasoning itself, not anything outside it.
The ox-herding sequence maps practice in stages: searching for the bull (true nature), finding its tracks, seeing it, catching it, taming it, riding it home, then forgetting the bull, forgetting both bull and self, returning to the source, and finally entering the marketplace with helping hands. The endpoint is not transcendent withdrawal but an ordinary return to everyday life and service, after even the goal and the seeker have dropped away.