Question 130
Bildert works in a cubicle in an office which consists of 27 cubicles arranged in a $3 \times 3 \times 3$ cube. Any two cubicles sharing a wall have a connecting door on this wall; for example, the corner cubicles have exactly 3 doors, while the center cubicle has 6 doors: one on each wall, one on the floor, and one on the ceiling. If Bildert starts at the central cubicle, can he visit each of the other 26 cubicles exactly once (i.e. without revisiting any cubicles)?