Koans: a common example is Hakiun Ekaku's "Two hands clap and there is a sound; What is the sound of one hand clapping?"
As a product of western logical and rational thought, I used to pat myself on the back, because I KNEW and could demonstrate the answer to the "one-hand-clapping" question.
You can do it yourself: Just slap your four fingers against the palm of the same hand.
Problem solved. Logic wins. What's the big deal?
The first time I heard this koan was from a buddhist writing professor. My answer to the-sound-of-one-hand-clapping exposed the pathways of my brain which didn't allow the absence of right or wrong answers. Ironically, those were the days I still threw logic out the window in favor of Christian myth and dogma. Such a logical answer revealed a mind that craved concrete, rational answers.
And that is the purpose of koans, whether used casually or during the practice of hard-core Zen meditation. They push and conjole the brain into new areas. The realization one settles on, or doesn't settle on, unveils the Present state of mind. Traditionally, if the answer matches the master's answer, one has gained a certain level of enlightenment.
For the purpose of Practice, I've left out the commentary that accompanies the following koan:
Goso said "A buffalo passes by the window. His head, horns, and four legs all go past. But why can't the tail pass too?" Case (koan) 38 from "The Gateless Gate"
O'Daly's introduction to Neruda's "The Book of Questions" suggests, "Neruda believed the inner quest was never-ending, that on some level what we learned was forgotten, so that we might learn it again.
Is forgetting the past in favor of the present a blessing or irony at its best?