Koan

In my RCIA class, one of the elect, who is a former Buddhist, explained a Zen Koan to me.  A Koan is a question, a statement, a puzzle, so to speak, to test the student's progress.

And so the student asked the teacher, "cat's bowl broken, why is the mouse smiling?"

The teacher referred to the class. 
Some just shrugged, "What's the point of this?" 
Some were curious and wondered why the mouse was smiling.
Some offered answers: the mouse broke the bowl, now the cat is unhappy which makes the mouse happy, the cat will get a scolding from his master, etc.

The teacher wondered if the mouse was simple-minded.  The mouse's knee-jerk response was to be happy because the cat was unhappy because his bowl was broken.  But if the mouse thought deeper he'd realize that if the cat wasn't eating from his bowl, the cat would soon turn to eat the mouse.  That smile would soon be wiped off the mouse's face.

This example explains a zen koan.  Teachers give koans to students to make them think.  A teacher can see how the student reasons and the progress he makes.  The koan really has no answer.  It is open to discussion to open the student's mind.