Use the buttons below each diagram to see a step-by-step walkthrough of each solution or explanation.

The easiest way to determine the solution to this puzzle is to notice that there are several dead ends and a few traps located with the temple, all associated with moving from beta tiles to alpha tiles, which close the gateways. Upon entering the temple, you cannot turn left and move down either of the two front hallways. The central hallway on the outer right (moving from the front to the back of the temple) is a trap: once you enter, you cannot exit in either direction.

This leaves the central hallway on the inner right the only viable option to move to the back of the temple and to the altar.

Again, examining the dead ends and traps will help us understand how to leave the temple from the altar. Expanding our view beyond the area around the entrance, there are several dead ends in the back of the temple. The areas that do not contain these dead ends, particularly the hallways along the front and very back of the temple, provide some indication of how to move around.

Turning right as you leave the altar, you need to make nearly a complete loop in the right rear of the temple, before traveling along the hallway in the very back of the temple (a few sidesteps are required to keep the gateways open). Then you can travel along the central hallway on the outer left, make nearly a complete loop in the left front of the temple, then go through the front hallway to the right front chamber which leads to the entrance.