A contribution to the Monthly Topic Challenge #3: Pencil and Paper Games series
This is another improbable story. If you want to skip it scroll to the bottom. The story is not necessary or even useful to solve it.
As Bob is watching over an archaeological excavation in Crete, Alice arrives in a hurry.
A: So what is the great discovery I absolutely need to see?
B: Oh, it is just ... The Lost Labyrinth of Knossos !
A: THE Labyrinth? The one built by Daedalus for King Minos to imprison the Minotaur?
B: Er ... the Minotaur part is a myth. It probably never existed.
A: Of course, but it is still King Minos's place, right?
B: Actually, I said the Labyrinth of Knossos. This place is named Knossos. And King Minos ruled in Knossos. So it is possible, but not proven, that this labyrinth belonged to King Minos of Crete.
A: OK, but how many labyrinths are in the region? It has to be The One. Speaking of which, I really want to see what it looks like. I'll take a big roll of string to be sure.
B: Well, you know, it was made of bricks. The cement degraded with time. And there were earthquakes. So it all fell to the ground.
A: Oh, damn! But you still can read the layout on the ground from where the bricks are? Right? I want to see what intricate patterns Daedalus designed in his creation.
B: The thing is, many bricks have been taken away to build other houses, except for the broken and funnily-shaped ones. You cannot really see where the walls were.
A: So, what you are telling me is that what you found is just a field of random bricks?
B: No, of course, it is ... a rectangular field of .. er .. random bricks.
A: Pretty much every building has a rectangular shape! What you found could be a storage place for grain, goods, or whatever. What makes you think it was a labyrinth? Did you make me fly to Crete for a pile of old bricks?
B: Er ... That is exactly why I need you. As I said, what is left behind are the broken and irregular-shaped bricks. And that is where it becomes interesting. Some odd bricks are T-shaped, L-shaped or X-shaped. I think L-shaped bricks were used in a corner between 2 walls. T-shaped bricks were used in the junction of 3 walls, and X-shaped brics were used at a junction of 4 walls. I carefully noted the location where these special bricks were found. It follows a nice square grid pattern.
B: But I can't figure it out. I need you to have a good look at my notes and show that this indeed is the layout of a perfect labyrinth.
Bob hands to Alice a pencil and a piece of paper
A: I am still mad at you. But somehow I like the challenge. Let me see. But we'll have a talk later.
In the image above, you need to reconstruct the plan of a perfect labyrinth built on a square grid.
A perfect labyrinth is completely connected. There is exactly one path between any two squares. There is no loop.
There is an entry at the left and an exit at the right.
The symbol at each intersection shows how the walls join at each intersection. An X marks a junction of 4 walls. A T marks the junction of 3 walls. An L marks a junction of 2 walls meeting at a right angle. Finally a dot marks a place where none of it applies. Either a wall goes straight thru or a wall stops at the dot.
A few wall are given: all outside walls and a couple of inner walls. The lowercase x marks a place where there is no wall.
As Alice hands the plan of the labyrinth to Bob, she says: "No, seriously? X-shaped bricks? Are you making this up? I hope this is not another of your practical jokes!"
Text version of the plan
L---∙---T---T---∙---T---T---∙---∙---L | | ∙ ∙ ∙ ∙ ∙ T ∙ ∙ L ∙ | | T L ∙ L ∙ ∙ ∙ T T T | | T ∙ L T ∙---∙ x ∙ T ∙ ∙ | | ∙ ∙ T L ∙ ∙ L L ∙ ∙ --> --> ∙ L T L ∙ L T L T L | | ∙ ∙ ∙ T T X T ∙ ∙ ∙ | | ∙ ∙ T ∙ ∙ ∙ T ∙---∙ ∙ | | ∙ ∙ T L ∙ ∙ L L ∙ ∙ | | L---∙---T---∙---∙---∙---∙---T---∙---L