A monastic once asked Zen Master Tozan, "Among the three bodies, which one does not fall into any category?" 

We should examine what is being asked here.

"The three bodies" refers to the trikaya, the three bodies of a buddha.  As I understand it, it is based on the concept that a buddha is one with the absolute while manifesting in the relative world in order to work for the welfare of all beings.  

The first of the three bodies, the dharmakaya, is the true nature of a buddha.  It is buddha nature itself, and is essentially ineffable.  It is the unified existence that lies beyond all concepts.  If you express it, that's not the dharmakaya.  The dharmakaya is our true self.

The second body is the sambogakaya, the "reward body," and is sometimes described as the experience of the ecstasy of enlightenment.  I have been told that Soyu Matsuoka has described the sambogakaya as the joyful realization of the dharmakaya and the nirmanakaya as one.

The third body, the nirmanakaya, or body of transformation, is the earthly body in which buddha's appear in order to teach and serve others.  It is represented by the historical person of Shakyamuni Buddha.

In Zen, the relationship between the three bodies is illustrated by an analogy of medical knowledge.  The dharmakaya can be compared to the great body of medical knowledge; the sambogakaya to the education of a doctor through which he or she gains that knowledge; and the nirmanakaya to the application of that knowledge in treating patients, who are thus liberated from sickness.  Zen teacher Gerry Shishin Wick explains that dharmakaya is wisdom, sambogakaya is the realization of wisdom, and nirmanakaya is the utilization of wisdom.

The trikaya are really three different views of the same reality and together constitute a whole.  They are just ways of talking about things, and ultimately, there are no three bodies - they are not three separate things, although each is a complete representation of the unified whole.

The monk asks Tozan which of the three bodies does not fall into any category.  I don't know how the monk even came to think that one of the three bodies defies categorization while the other two don't, but he's already lost in delusion.  He's asking the wrong question.  It's like asking "What is the marital status of the number seven?  Is it married?  If not, is it therefore single?  Or is it somehow neither (or both) married and single?"  These are the wrong questions, and there's no merit to contemplating them.

Our minds assign name and form to the nameless, formless universe, and we then come to believe that the cookie-cutter pieces of reality that our minds have tried to separate from the unified existence are actually separate existent or nonexistent "things."  This is what the monk is trying to do with the the buddha dharma - slice it and dice it into separate entities, and then hold each one up for examination to compare and contrast with the others.  By acknowledging that there are things that do not fall into categories, he's further created "things" called "categorical" and "non-categorical."  He's created a "thing" not only out of nothing, but out of "no thing."

Zen Master Tozan will have none of this.  He tells the monastic, "I am always sharp at this concrete place."