SPOILER ALERT. This section contains solutions.
The Path
The Path includes the rooms found along the shortest path from Room 1 to Room 45 and back to Room 1. (This series of rooms is referred to as the True Path.)
Additionally, the Path includes four room that do not lie along the True Path, but from which one can return to the True Path without returning to Room 1. What distinguishes these rooms from the Loop is that once one has entered the Loop, it is impossible to return to the True Path without returning to Room 1 through Room 41.
The Loop
The Loop is a group of 19 room from which one cannot return to the Path except by returning to the beginning, Room 1, through Room 41. Loop rooms can, however, lead into the Trap.
The Trap
The Trap is a group of seven rooms such that, having entered any one of them, one cannot access any other rooms in the Maze. Entering the Trap in effect ensures that one has failed to complete the Maze. Within the Trap is Room 24, the only room that has no exits and brings the game to an end.