Maze

The Maze is one of humanity’s oldest puzzle formats — physical mazes (labyrinths) date back to ancient Egypt and Crete (the famous Labyrinth of Minos). As an interactive puzzle game, the Maze tests navigation, spatial reasoning, and patience. This game offers procedurally generated mazes that you traverse from start to finish — simple, meditative, and infinitely replayable.

How to play

• You’re placed at the start position of a maze.
• Arrow keys (or WASD) — move one square at a time in any direction (north, south, east, west).
• Walls block movement.
• Reach the end position to solve the maze.
• Maze sizes scale from 10×10 (easy) to 50×50 (challenging).
• Time and step count are tracked for performance grading.

Beginner strategy: the Right-hand Rule

• Always keep your right hand on the wall as you walk. Eventually you’ll reach the exit (or return to start).
• This works on simply connected mazes. Standard generated mazes work with this rule.
• Not optimal but guaranteed. The right-hand rule may traverse the whole maze before finding the exit — long, but successful.
• Equivalent: left-hand rule. Same idea, opposite hand. Both work on standard mazes.
• Fails on multiply-connected mazes (mazes with loops). Most generated mazes are simply connected.

Intermediate strategy: dead-end elimination

• Identify dead ends. Cells with walls on 3 of 4 sides are dead ends.
• Mentally mark dead ends. Once entered, don’t revisit.
• Trace the “spine.” The path from start to end is the maze’s spine; everything else is dead-end branches.
• Backtrack efficiently. When you hit a dead end, retrace to the last decision point and try a different direction.
• Look ahead. Before committing to a corridor, glance further to see if it leads somewhere.

Advanced strategy: maze structure

• Tremaux’s algorithm. Trace paths and mark them. Avoid retracing fully-explored corridors. Always solves any maze efficiently.
• Random mouse algorithm. Random walks eventually solve any connected maze (in exponential time). Inefficient.
• Pledge algorithm. Works on mazes with loops by tracking signed wall-following counts.
• Dijkstra/BFS for optimal pathing. Top maze solvers mentally trace shortest paths using graph-search intuition.
• Speed solving. Top maze racers complete 30×30 mazes in under 60 seconds.

Maze types

• Simply connected: no loops; right-hand rule solves them.
• Multiply connected: has loops; right-hand rule may fail.
• Weave maze: corridors can pass over and under each other (3D-like).
• Spiral maze: corridors spiral inward.
• Theta maze: circular concentric rings.
• Hexagonal maze: hex cells with 3 walls each.

Maze generation algorithms

• Recursive backtracking. Carves paths through walls using DFS. Creates highly branching mazes.
• Prim’s algorithm. Random wall selection. Creates more uniform, less branching mazes.
• Kruskal’s algorithm. Union-find based. Even more random.
• Wilson’s algorithm. Loop-erased random walk. Statistically perfect mazes.
• Recursive division. Divides space into sub-regions with corridors.

Maze history

• Ancient Egypt: labyrinth at the Hawara pyramid complex, ~1900 BC.
• Crete (1700 BC): the legendary Labyrinth of Minos. Greek myth.
• Medieval Europe: cathedral floor labyrinths for spiritual contemplation.
• 17th century — hedge mazes: ornamental garden mazes in England, like Hampton Court Palace’s 1690 maze.
• 1973 — Pac-Man (proto-maze game). Inspired by physical mazes.
• Modern era: mazes in countless video games, puzzle books, and AI research benchmarks.

Common mistakes

• Wandering without strategy. Random movement is slow and frustrating.
• Not marking dead ends. Re-exploring dead ends wastes huge time.
• Ignoring the right-hand rule. Simple but guaranteed to work.
• Rushing through corridors without looking. Always glance ahead.

Variants

• 3D mazes. Multiple floors with stairs.
• Themed mazes. Pac-Man, Zelda dungeons.
• Logic mazes. Where wall colors affect navigation rules.
• Time-limit mazes. Race against the clock.
• AI maze solvers. Standard introductory CS exercise.

FAQ

• Q: Does the right-hand rule always work? A: On simply connected mazes, yes. Not on mazes with loops.
• Q: Is there an optimal solution? A: For every maze, yes — the shortest path. Finding it requires graph search.
• Q: What’s the fastest solving approach? A: Tremaux’s algorithm — wall marking + backtracking — guarantees efficient solution.
• Q: Are all mazes solvable? A: Yes — if a maze has a connected start and end, a path always exists.

For other navigation/puzzle games, try Sokoban, 15 Puzzle, Pacman, or Tower of Hanoi.