A Zen puzzle garden (ZPG) is a grid of squares that fall in three groups: walkable squares, where a monk may move freely; rock squares, which cannot be entered; and sand squares, where the monk may move according to certain rules. The problem is to decide if in a given ZPG there exists a walk for the monk that covers all sand squares. This paper shows that the problem is nondeterministic polynomial-time (NP) complete by means of a polynomial-time reduction from the Hamiltonian circuit problem for cubic planar graphs. The proof is very short and also fairly simple in comparison with many other NP-completeness proofs. No argument is included for why the given construction works. Apparently, this is regarded as obvious, but it may take some time to check.

The initial explanation of the rules for the walk seems to lack clarity at several points and will probably leave questions for someone not yet familiar with the topic. For instance, it is not stated explicitly that rock squares must not be entered.