Wumen frames the single word 'Mu' (No) as a checkpoint that cannot be passed by reasoning, affirmation, or negation; the student is told to hold it continuously until intellectual approaches exhaust themselves. The point is not to answer the question but to bring discursive thinking to a dead stop so that insight can erupt from somewhere other than analysis.
Each case pairs an irresolvable prompt with commentary and verse, a structure designed to frustrate the problem-solving mind rather than satisfy it. By refusing a rational solution, the koan converts the student's own striving into pressure that is meant to force a shift in how perception operates.
When two groups of monks quarreled over a cat, Nanquan held it up and demanded someone 'say a word' to save it; when no one responded he cut it in two. The episode illustrates that a moment demanding a direct, non-deliberating response is lost the instant it is treated as a puzzle to be debated.
The commentaries repeatedly warn that words, verses, and even the koans themselves are devices that indicate something and are never the thing indicated; mistaking the instruction for the realization is the central error students make. Viewed this way, every teaching is provisional scaffolding to be discarded once it has done its work.