**The Path: **The upper level contains nineteen rooms, the rooms of the 16 room path (one is visited twice) and four side rooms off of the Path. The only way to enter the Path is from room 1. Most doors on the Path exit to the Loop or the Trap.

### Navigate by clicking on numbers.

- Images Copyright 1985 by Christopher Manson.

Looking at this map helps me understand why this book is so hard. The structure of the Maze is what makes it so hard.

A lot of the problem is with Room 4, the Great Hallway with the False Face of the sun. Room 4 has seven doors leading out, the most of any in the Maze. You have to pick the exact right one to proceed; there are no branching paths here that both lead to the right place eventually. Of the six wrong doors here, three lead straight to the Trap, and the other three lead to a path (either on the Path or the Loop) where the best you can do is go through a lot of steps to get back to Room 4 again.

Let’s say you choose the correct door, and now you’re in Room 29. You now have to find the secret door. Bear in mind that there are four non-secret doors in this room to distract you as you try to choose between them. If you don’t find the secret door, what happens?

If you leave Room 29 without finding the secret door, there are four things that can happen.

1. You end up in the Trap.

2. You end up on the Loop.

3. You end up back in Room 4, the Great Hallway.

4. You end up back in Room 29 without passing through Room 4.

I have calculated the probability of each of these.

Trap: 52.08%

Loop: 41.67%

Room 4: 3.47%

Room 29: 2.78%

(These probabilities are based on the assumption that the reader doesn’t go back to the room they immediately just came from by going back through a two-way door, and chooses at random besides that).

If you end up back in Room 4, you’ll probably end up going through the wrong door instead of going to Room 29 again. You may even deliberately avoid Room 29 since it led you in a circle. Still, if we assume a 1 in 7 chance of going back to Room 29 once we make it to Room 4 and add that to the chance of getting to Room 29 without Room 4, we’re up to a 3.27% chance that you end up back in Room 29 if you leave through the wrong door.

So if you make it all the way through Room 29 but don’t find the secret door, you only have a ONE IN 31 CHANCE of getting back to Room 29 for another chance that you’ll notice the hidden door this time. This does not include the chance of getting back to Room 29 after a long journey through the Loop.

The part of the Path on the “right” side of Room 4 on the Path map that you can get to without finding the secret door is only five rooms, and all of the doors between these rooms are two-way. So figuring this area out should be easy, right? Wrong.

One type of person who is likely to see Room 29 again more often than this is a completionist who tries to exhaust every possibility – someone who realizes that making it to Room 4 is good, and wants to exhaustively figure out every option coming from every room that Room 4 leads to. (Admittedly, it isn’t that hard to figure out that going through Room 4 is good.) There are two big problems with this approach.

1. You are going to spend a LOT of time in the Loop, probably both before and after finding Room 29.

2. If you approach a room from the perspective that you are going to brute force the Maze, jumping through each door with a sense of curiosity so that you can explore where they all lead, rather than carefully studying and puzzling over each room, you are more likely to miss the hidden door.

I would also point out that the probability of making it directly to Room 4 via the shortest path if you choose at random is one in 320. So it’s a tough thing to even get to the point where you have to address all of this. The total probability of getting to 4 probably isn’t that much better than the chance of getting there directly, since the longer a path is, the more chances there are to fall into the Trap or the Loop.

Even if you eventually figure out that the Loop is a waste of time that sends you in circles, the problem is that the Path is ALSO a waste of time that sends you in circles without the secret door. The “left half” of the Path that contains Room 1 is a loop, and the “incomplete right half” of the Path is a loop that goes 4->29->8->12->39->4.

Even if you figure out that there is hidden door somewhere in the maze (perhaps because you cheated by flipping through the book and figured out that the only rooms that lead to 45 are 17, 28, 23, and 32 indirectly, and that there are apparently no doors that lead to any of those rooms), you have no way of knowing whether it is in the rooms that form the Loop or not. If you explore looking for a secret door, the structure of the Maze is likely to lead you to the Loop. Even if you cheat and just flip from one page to the next looking for a secret door, there are more non-Path rooms than Path rooms.

The secret door is in a poorly lit room that doesn’t even immediately jump out from its appearance as a great room to be in, or an especially important room. Maybe something seems odd about it that might be significant, but that’s the case in every room. Even if you notice something on the table that looks like an upside-down 17, there are all kinds of letters and hidden messages in the Maze and whatnot that are not the label over a door.

There are also a lot of obvious doors with no numbers on them that are the back end of a one-way door, and some of them have symbols over them. If you think there is a secret door in the Maze, you may mistakenly think that it involves a way to somehow go through one of those doors.

I love this book because of how much I hate it!

I’ve enjoyed your structural analysis here and elsewhere. You should participate in some kind of MAZE-based webcast.

Novice,

This really illustrates Manson’s ingenious system for keeping the reader confused. Only a 1 in 31 chance of returning to 29! Finding the hidden door without stepping outside of the game would indeed have been highly unlikely!

The chances of making it back to Room 29 after leaving it are higher if the player considers the possibility of going back through a two-way door to the room they were just in.

One of the few things about the Maze’s structure that seems remotely merciful is the structure of which doors between two rooms in the same “realm” are one-way versus two-way. Arguably, this is by definition, since a two-way door from a Path room means you are in a true Path or side-Path room, while a one-way door from a Path room means you are in the Loop at best unless there is another door to a Path room other than Room 1.

Obviously, it is unmerciful that all doors from the Path to the Loop, all doors from anywhere outside the Trap to the Trap, and all doors to the Abyss, are one-way. However, on the Loop, most doors that lead the wrong way are two-way, while many doors leading the right way are one-way. (Admittedly, a few one-way doors to the wrong room exist as well.) Similarly, on the Path, some of the doors that lead the right way are one-way, but if you go to a side room or to a part of the Path you aren’t supposed to go to yet, the door is virtually always two-way.

Even in the Trap, the fact that all doors except the one to the Abyss are two-way makes the Trap the easiest of the three realms to figure out the structure to by far, making it easier to realize you’re trapped the next time you go through the Maze and end up in a Trap room you recognize. If you merely memorize “stay out of Room 24″, you will eventually realize that the Trap is a Trap the very first time you visit it with the intent to avoid 24. If you don’t consider this cheating or think it is but don’t care, even a player who had done no real mapping could easily write down the numbers of all the Trap rooms and avoid them.

One exception to the mercy is the way the game forces you to leave after reaching Room 45 by a significantly different route than you came. It would be too easy if all the doors leading there were two-way and you could just come out the way you came in!

Novice, it is hard to tell sometimes, but Vince was extending a sincere invitation there. We would love to talk to you! Contact us through Mazecast [dot] com (there’s a “contact us” form on the home page) if you would like to chat or subject yourself to being interviewed on air about your thoughts on MAZE. It will hardly hurt at all — promise!

(Same invitation goes out to anyone on here interested in connecting. Get in touch!)

@ White Raven Well, you could still find it the first time. The odds he posted were the odds of coming back afterward.

Nick,

Novice’s point was based the premise that a person would not find the hidden door the first time…which is a good bet.

The drawing of the Path has an error. It shows the entrance from Room42 to Room 25 as a Trap entrance. It is actually a Loop entrance.

It seems like the handful of entrances to the Loop that lead to Loop rooms that lead back to Room 1 quickly rather than slowly are all in the half of the Path that are on the Room 1 side of Room 4, while all the Loop entrances from Room 4 and from the Room 45 side of Room 4 are to rooms that require a very long journey back to 1.

Novice,

So it does! Thanks for the proof read! I will fix the error when I get a chance.

I have compiled a list of MANDATORY moves if you are trying to get to Room 45 and back but don’t care about doing so by the shortest path or seeing all the rooms on the shortest path.

GETTING TO ROOM 45

1. Choice 1: You must go from Room 1 to Room 30. You should go 1 ->26->30 but can go 1->20->5->30.

2. Choice 2: You must go from Room 30 to Room 42. The obvious and best way is to go directly. The other option is to through 15 and 37.

3. Mandatory move 1: You must go from 42 to 4.

4. Mandatory move 2: You must go from 4 to 29.

5. Mandatory move 3: You must go through the secret door from 29 to 17.

6. Mandatory move 4: You must go from 17 to 45. [obvious move once you are in 17]

GETTING BACK

Getting back can be done in many ways, since the Loop leads to Room 1. However, if you go to any of the Loop rooms that can be accessed from the second half of the Path, you are going to be making a long journey in which almost every move is a mandatory move. (Most of the time, a wrong move can be reversed by traveling back to where you were before and won’t send you to the Trap, but there are a long series of exact doors that have to be taken to get back to1).

If you want to get back using Path rooms, here is what you must do.

1. Choice 1: You must go from Room 45 to Room 23. You should do so directly, but can do so through Room 28.

2. Mandatory move 1: You must go from Room 23 to Room 8.

3. Choice 2: You must go from Room 8 to Room 12. You should do so directly, but can go through rooms 29 and 2.

4. Mandatory move 2: You must go from Room 12 to Room 39.

5. Mandatory move 3: You must go from Room 39 to Room 4.

5. Mandatory move 4: You must go from Room 4 to Room 15. [You're on the home stretch! There aren't even very many ways to get to the Trap from this point.]

6. Choice 3: You must get from Room 15 to Room 20. The best route is to go 15->37->20. However, you can also go 15->30->5->20. You can ALSO get to Room 37 or Room 30 indirectly. Regardless, you must either get to Room 37 and take the door to Room 20 or get to Room 30 and take the doors to Room 5 and then Room 20.

7. Mandatory move 5: Take the door from Room 20 to Room 1. [Obvious move.] Congratulations!

Excellent! Well done analysis!

MAZECAST S02E03 – WALKING THE PATH

youtube.com/ watch?v=jIM_VAT2stc

Out now. Brent swiftly goes through the path, mentioning the most apparent clues to get to the next room. Good refresher for people who don’t want to get bogged down in details. Good for newbies who want to get a general sense of the Maze path and don’t care about spoilers.

Rooms 2, 5, 28 and 32, are not part of the 16 room path, they are side rooms off of the path. What this means is that these rooms are connected to the path. You can return to the path from these 4 rooms.