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.
Connect matching nodes across the topological grid.
Solve the built-in campaign levels.
Design, customize, and save your own grids.
Manage, share, and track your solutions.
Design custom paths for different tile geometries.
Explore the combinatorics and topology behind easy, hard, and impossible grids.
A mathematical lens on size, structure, solvability, and why local tile rules transform global difficulty.
Core idea
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.
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.
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.
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.
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.
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.
Manage grids, retrieve saved progress, and view solutions.
localStorage.Level 1 - Route the matching letters
All paths perfectly routed.
Configure grid โ drag letters to boundaries โ save to repository
Design custom routing logic for any geometry.
Drag tiles onto ๐๏ธ to delete them permanently.