Commenter HistoricalLing does have a point. Katsuki Sekida explains:

"Now, 'Mu' means 'nothing' and is the first koan in Zen. You might suppose that, as you sit saying 'Mu', you are investigating the meaning of nothingness. But that is quite incorrect. It is true that your teacher, who has instructed you to work on Mu, may repeatedly say to you, 'What is Mu?' 'Show me Mu,' and so on, but he is not asking you to indulge in conceptual speculation. He wants you to experience Mu. And in order to do this, technically speaking, you have to take Mu simply as the sound of your own breath and entertain no other idea."

In Zen practice, the purpose of a "koan" is to occupy the mind with a fruitless question (or in LW parlance, a wrong question). (Although "Mu" isn't even a question!) This helps the meditator to maintain concentration, since by dwelling on a dead-end like "What is the samadhi in particle after particle?" he isn't distracted by the normal flux of flitting thoughts.

The student is still expected to provide an answer, eventually, but not one arrived at by rational thought—rather, it is supposed to strike him spontaneously. Of course, this isn't a generally wise approach to answering questions; but if the Zen master were to tell his student that the koan can't be answered, he might not take the exercise seriously. (I expect that Bayesians find it difficult to meditate using koans, since they are so keenly aware of wrong questions.)

A koan is a deliberately futile question, generally short and intended to obscure thought. To use this word also to refer to puzzles which are not skew to reality and which are intended to be answered sensibly, is likely to cause bad inferences about the purpose of koans in Zen—and is jarring in this context!