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PATH PUZZLE

Connect matching nodes across the topological grid.

โ–ถ Play Game

Solve the built-in campaign levels.

๐Ÿ› ๏ธ Level Editor

Design, customize, and save your own grids.

๐Ÿ“ Repository

Manage, share, and track your solutions.

๐ŸŽจ Tile Forge

Design custom paths for different tile geometries.

๐Ÿ“ Path Theory

Explore the combinatorics and topology behind easy, hard, and impossible grids.

Path Theory

A mathematical lens on size, structure, solvability, and why local tile rules transform global difficulty.

Core idea

LARGER GRID != Harder Solution

Size alone does not determine difficulty. A larger board can be easier if it creates more routing slack, more alternate corridors, or fewer forced collisions. A smaller board can be brutal when a handful of local choices controls the entire network.

In other words, hardness often comes from structure, not scale: bottlenecks, endpoint ordering, symmetry, local rigidity, and how much freedom each tile preserves for the rest of the puzzle.

Existence of solutions

Before asking for the best route, ask whether any valid route exists at all. Boundary placement, disconnected regions, narrow bottlenecks, and forced pairings can make a puzzle impossible before the search truly begins.

Number of solutions

Some grids collapse to a single rigid routing. Others admit many valid completions. Counting solutions tells us how constrained a puzzle really is, and whether the challenge comes from logic, exploration, or ambiguity.

Simplest solution

Among all valid routings, which one is the cleanest? Simplicity might mean fewer turns, fewer detours, more symmetry, or more natural pairings. The simplest solution is not always the one that is easiest to discover.

Why do two-path tiles feel so hard?

The key issue is flexibility. A two-path tile makes each placement a strong commitment, and those commitments propagate across the board. A three-path tile changes the global behavior because it introduces more slack, more rerouting options, and fewer brittle dead ends.

Two paths per tile

  • Each tile creates tight pairings between edges, so every rotation matters more.
  • A wrong local choice can force a contradiction much later, far from where it began.
  • Bottlenecks become severe because there are fewer alternate ways to continue a route.
  • The puzzle becomes more rigid, so the whole board can hinge on a small number of cells.

Three paths per tile

  • More internal connectivity gives routes extra ways to continue through crowded regions.
  • Local mistakes are easier to recover from because the system has more slack.
  • Forced contradictions appear less often, so the puzzle can feel less brittle.
  • The raw search space may grow, but the practical difficulty can drop because constraints are weaker.

That is the interesting tension: more options do not always mean a harder puzzle. Sometimes extra connectivity increases the number of states while making the global routing problem easier to satisfy.

Questions worth exploring

Level Repository

Manage grids, retrieve saved progress, and view solutions.

๐Ÿ“ About Local Memory:
Your custom levels and saved routes are stored in this browserโ€™s localStorage.
โ€ข They survive restarts and normal browser updates.
โ€ข They are removed if you clear site data, switch browsers, or use private browsing.
โ€ข Winning a custom level auto-saves a solution.
โ€ข Export a level code if you want a portable backup.

Hex Path Puzzle

Level 1 - Route the matching letters

๐Ÿ—‘๏ธ [ DROP BOARD TILE TO DELETE ]

LEVEL CLEARED!

All paths perfectly routed.

1. Place: Drag a tile onto the board, or click an empty cell then click a tile.
2. Move / Replace: Drag a placed tile to another cell to move or swap it.
3. Rotate: Click a placed tile to rotate it; some cells restrict the allowed angles.
4. Remove: Use Remove Selected, or drag a placed tile into the red Trash Bin.

Level Editor

Configure grid โ†’ drag letters to boundaries โ†’ save to repository

Endpoints

๐Ÿ—‘๏ธ [ DROP LETTER HERE TO DELETE ]

Tile Forge

Design custom routing logic for any geometry.

Saved Custom Tiles

Drag tiles onto ๐Ÿ—‘๏ธ to delete them permanently.