Wrap-up: The Making Of Magic Maze Puzzle
This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.
Caution: This post may contain spoilers.
This puzzle originates from a competition to invent a new genre of logic puzzle which involved moving objects. I initially asked whether a chess puzzle would count, but obviously there's a wide literature of chess puzzles so it would be hard to guarantee my genre was indeed new.
At the time of making this puzzle, I had recently been to a board game store with friends and played Magic Maze, which I found fun. After thinking for a while about possible board games out of which I could make a puzzle, I settled on that.
To start with, I needed to work out a suitable subset of the rules to implement, since Magic Maze has a lot of rules, and then some as you play the harder 'levels' of the game. Obviously a key part of the game was the revealing of tiles, so some sort of revealing was required. But since a logic puzzle has to have perfect information, it was important that all tiles were visible. As a result, I decided to make a custom set of tiles, with the stack in a predetermined order (you aren't able to choose the order of tiles in the game, and allowing for that would have made the logic of which tile to choose next almost impossible).
It also quickly became clear that allowing arbitrary moves wasn't a possibility. So I had two options: choose a fixed order of tokens, or choose a fixed order of move types. Given that you could break a long move in one direction into shorter moves, a fixed order of tokens seemed infeasible, so I chose a fixed order of move types - given that different directions and searching new tiles were split up among different players in the base game, I decided that the moves would be N, E, S, W and search. Also, I decided pieces couldn't occupy the same space twice as this would have been too difficult for me to picture.
At this stage it was probably possible to construct a similar puzzle to what I have now, but there were still limitations in that one could relatively easily reorder the movement stages of tokens among several "cycles". As a result, I chose to include "stairs" (in the base game I believe they're escalators, but I didn't want to make detailed drawings) - these would provide more constraints on where tokens were at particular times. I decided on the order at this stage up to cyclic rearrangement, spacing out each pair of stairs/search, N/S and E/W.
Finally, I decided to adopt the premise of the game that you have to move all the tokens to "shops" (triangles) at the same time, and then to "exits" (squares) - this seemed like it would be constraining enough while still being interesting.
Obviously, to easily draw things, I needed some sort of grid. To account for the endless backtracking that looked like it would be necessary at the time, I decided to do this on my computer, and thus I needed the ability to stroke-erase and undo a lot. My choices were some Adobe product or OneNote, and being more familiar with the latter (which I do a lot of online puzzles on as well), I chose that.
It was time to design the first tile. In accordance with Magic Maze, it would be 4 by 4, and the exits would be on the right-middle edge of each side. Also, stairs seemed quite necessary with the move ordering constraint, and all four exits need to be open (I didn't want a triangle or square on this tile). I also chose to have a symmetrical layout on each tile. Finally, in accordance with the game, I decided that the tokens should initially occupy the central 4 squares. So I made a first draft:
Once I had settled on this design, I finally had the motivator that would get me going. Logic proceeded smoothly, until around tile 4 where I was a bit stuck. To get the last two pieces out of the centre tile required a few moves in a certain order which was "backwards" compared to the cycle I had arranged, so I needed places to dump a lot of moves. This was tile 4, and that's why it looked so crazy.
There was also an ambiguity over which of tile 4 and 5 would be placed in which place. As a result, I made one of my first "deeper" arguments in this puzzle, which was that with tiles 8, 9 and 10 closed except for moving "straight", it would be impossible for two tokens to get to the two squares on tile 4.
As I got more familiar with the movement of the pieces, I was able to foresee somewhat deeper consequences of some moves. I also realised the final move-counting argument seen by Dr Xorile at this stage, and as a result I found that the ending was actually quite constrained even with few walls (e.g. see tile 7), so I only had to make sure some set of moves actually allowed for the finish. (Of course, tiles 8, 9 and 10 were necessarily inconsequential, as determined back at tile 4.)
(Click for better resolution)
After a couple of rounds of testsolving, I edited a bit for uniqueness (some extra variations I hadn't seen caused me some trouble, but luckily they were "far enough away" from the main line that I could mostly add one wall and remove them), and then removed some unnecessary walls in the first 7 tiles. Reasonably convinced that it was unique, I prettified it and sent it off to the competition.
(I sent off the light version because it's easier on printers, but I like the dark version better...)
The puzzle was much better received in the competition than I initially thought it would be given its complexity, though it did take a couple of people solving it and recommending it for it to kick off (the competition had anonymous submissions for voting purposes, so I couldn't endorse it). One solver used LaTEX to tidy my rough scribbles up, which made it look a lot more presentable - thanks for that! It also seems to have been popular here on Puzzling.
In terms of solving methods, some people printed it out (with, I think, one laminating the LaTEXed version). Others used tools such as GIMP and I am really impressed with the pair that did it in Google Sheets!
(Click for better resolution... doesn't this look like fun to set up!)
I guess I wish I could have made a better title - I wanted "Magic Maze" and thought appending "Puzzle" seemed a bit artificial, but "Magic Maze" doesn't meet the 15 character limit. I initially thought that the rules were too convoluted to understand anyway, even after simplifying, but it appears not. Hopefully a few more people have actually tried solving it - and if you did so, I hope you liked it! (With this format, it's pretty tempting to click on the solution, I guess...)
It would be pretty interesting to try this with a different set of actions: a few more are available in the base game, and yet more with expansion packs. Portals, anyone? I also wonder whether an interesting puzzle could be made without stairs: as mentioned above, they were somewhat of a convenience measure for me as the puzzlewright.