In this teisho, Peggy Metta Roshi takes up case 1 in the Gateless Barrier:

A monk asked Chao-chou, “Does a dog have Buddha nature or not?”

Chao-chou said, “Mu.”

Peggy Metta Roshi comments:

Does the questioner understand what he or she is asking? What is she asking? And how could a single word – Mu – open that door, resolve this monk’s inquiry, and transform his life – and yours, and mine, and all beings’ across time and space? If this whole thing confounds you, then you are approaching it correctly, and you are in the right place.