📖 Labyrinth

Unicursal Labyrinth

A labyrinth that has no branches, thus only a single route from the start to the end, is called a unicursal labyrinth. These don't present any inherit challenge to the player as there are no choices to make. However, they can present a thematic backdrop and serve to confuse the player as to where they are.

They also show up in ropes and knots puzzles, where you have a series of overlapping paths between a series of starting and ending points. There are no branches, instead the player is challenged to stay on the correct path to find the ending point that matches that connects to the starting point.

Additionally we can find path-like structures are decoration in a game world. They may not be solvable, or be trivial and repeating, when used as a decorative element.

Constraint Logic

A puzzle can eschew walls in favour of constraint logic. In this type of labyrinth, the player's path is determined by a series of constraints, or rules, about their movement.

For example, a player may need to move a knight on a chessboard. Only the typical L-shaped moves are allowed. The player may also need to keep the knight safe at all times, thus can never move into a position where it could be killed.

Or in my puzzle Crate Treasure the rules are present as a series of symbols that somehow match what is in the maze. In this form, the player must find the final crate.

Dynamic

In a dynamic labyrinth the walls, or the actions, change in response to other actions.

Path Finding

The key ability to resolve a labyrinth is path finding. This is where the distinction between some puzzle types can be tricky. Path finding applies to a lot of puzzles that don't ostensibly look like labyrinths, but in essence are.

For example, consider the classic puzzle where a farmer needs to take his wolf, goat, and cabbage across a river in a canoe. This puzzle can be represented as a series of positions with paths between them (like a series of rooms and doorways). Constraint logic adds rules, such as the wolf would eat the goat is left together. This puzzle is a virtual maze, as the player needs to navigate through a series of positions, finding the correct sequence that doesn't violate any of the rules.

A labyrinth, like the river puzzle, can be reduced to a series of nodes and edges. Each node represents a place, either a physical location in the maze, or state of affairs for the river crossing. Each edge represents a path between nodes, either a hallway in a maze, or the action taken in the river crossing. Edges are nodes create graphs, something that is well explored in mathematics with graph theory. All puzzles that can be reduced to nodes and edges are naturally related to each other.

Yet, we don't typically consider the river puzzle to be a labyrinth, despite using the same general technique of path-finding. The theme of the puzzle makes it feel different, though there is no clear divinding line between what is a labyrinth and this more generic form of puzzle. We assume that a labyrinth involves a physical manifestation of hallways and rooms. It must be something tangible. Whereas the river crossing puzzle each state is virtual and can't exist on its own — it's a series of locations that morph in time.