Once upon a time, somewhere in Italy, two archaeologists unearthed a buried passage.
As they explore the passage they reach the doorway which is clearly the entrance of a wide structure behind. They see well-built passages made of square stone walls. There are passage branching in various directions.
One of them exclaims:
-- It's a maze!
And indeed, it is. Very excited about their finding, they want to explore it. They start arguing about the best way to proceed without getting lost. But they stop when they see the following engraving on the wall.
-- Look at this, a map! Not much of a challenge. I'm a bit disappointed. What's the point of building a maze if you just put the full map at the entrance? That doesn't make any sense! Well, let's see what is at the other end.
The other doesn't reply, absorbed in his study of the engraving, scribbling on a notepad. Eventually he gasps and becomes pale.
-- That's not a map, it is a message. It is a warning!
-- A warning?
-- Yes, I know where this maze ends, and we definitely shouldn't go there!
From what you have seen and what you have read, can you tell me what the message says and where to the maze is leading?
Forget steganography, hidden pixels or color filters. If you copy the maze on a notebook it should be good enough to solve it.
╶─────────┬───┬───────────┬─────╮ ╷ ╶─────┬─┴─╴ ├─┬─╮ ╭───┬─┤ ╭─╮ │ │ ╶─────┴───╮ ╵ ╵ ╵ ╰─╮ ╵ ╵ ╵ ╰─┤ ├─────┬─╴ ╷ ╵ ╶─────┬─┴─╴ ╭───╮ │ ├─╴ ╷ │ ╭─╯ ╶───┬─╴ ╵ ╭───┼─╴ ╵ │ │ ╶─┼─┼─┤ ╶─┬─┬─┴─────╯ ╶─┴─╮ ╶─┤ │ ╶─┤ ╵ │ ╷ ╵ ╰─╮ ╶─┬─╴ ╭───┴───┤ │ ╶─╯ ╷ ╵ ╰─────┴─╴ │ ╶─┴─┬───╮ │ ├─────╯ ╶─────────┬─┴─┬───┴─╮ ╵ │ │ ╶───┬───╮ ╭─╴ ╷ ╵ ╷ ╰───╮ ╰─╮ │ │ ╶─╮ ╰─╴ ╰─┴─┬─┴───┤ ╶───┴─╴ ╵ │ ├─╴ │ ╭─────╴ │ ╷ ╷ ╵ ╶─────────╯ ╰───┴─┴───────┴─┴─┴─────────────╴
-- A warning? What does it say?
The first archaeologist just shows his notepad. At the bottom you can see 3 lines of text, nicely aligned, 11 characters in width. The second one reads it and agrees.
-- If this is correct, we better get out of here.
-- But how did you even think it could be a message?
-- It is the ... well ... entropy of the map. There is no symmetry, no long corridors, the branching pattern is complex, there are way to many short dead ends. That is not how you build a maze. Looking at the map I could see that its complexity is uniform. I felt that the placement of each wall conveys hidden information.
-- I can't say I got that feeling. Is it so?
-- Yes. As I discovered, no wall is placed just randomly. Every single wall contributes to the message.
They are now on the surface, back to the car, eating a sandwich before hitting the road.
-- Funny the thing you told me earlier. I never realized that.
-- Which one? I am always funny.
-- Yeah, well... debatable. Anyway. It was about the pillars and the walls. That there are exactly as many pillars in a labyrinth as there are walls between the pillars.
-- That's true for every perfect maze. But that is not interesting. The interesting part is that one can match pillars to adjacent walls in a perfect one-to-one relationship. It is like one pillar with one wall form a unit.
-- Interesting... You give me an idea. If we want to go into the business of building prefabricated mazes, we just need to produce one type of piece, a pillar with an attached wall? That would work for every possible labyrinth? You never need an extra pillar or an extra wall?
-- Exactly. You still need to build the outer wall, of course.
-- We can subcontract that.
-- OK. There is still something I don't get. When you display a warning, you want to make it readable, right? Like bright yellow text on red background. What sense does it make to display it in such a cryptic way?
-- I can only guess that warning is a legal requirement. And they don't like it. So they found a loophole to comply without really complying.
-- They must have found the one lawyer who could think of such a thing.
-- I bet they are not short of that kind.