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.
Continue the campaign, or generate a fresh board with your chosen geometry and difficulty.
Play the built-in curated levels exactly as before.
Use the default tiles for a generated board. Choose the geometry, layers, pairs, and difficulty from a dedicated random panel in the game view.
A mathematical lens on size, structure, solvability, and why local tile rules transform global difficulty.
Further thinking
A path puzzle is not only about finding a route. It invites deeper questions: Does a solution exist? Is it unique? What makes one puzzle elegant, another impossible, and another surprisingly hard?
These questions bring together geometry, topology, and combinatorics. They also show why puzzle difficulty comes from structure, not just size.
Before solving a grid, we can ask whether it is solvable at all. Some boundary placements force success, while others create hidden contradictions, bottlenecks, or dead regions from the very beginning.
Some puzzles have a single beautiful route. Others allow many. Counting solutions helps us measure rigidity, freedom, and how much logic the puzzle truly demands.
Among all valid routings, which one feels most natural? “Simplest” might mean fewer turns, less backtracking, more symmetry, or the cleanest overall picture.
Difficulty often comes from tight spaces, forced moves, endpoint ordering, symmetry traps, and local choices that affect the whole board. A larger grid is not always harder; sometimes it simply gives more room to breathe.
A two-path tile is restrictive: each placement is a strong commitment. In a two-dimensional grid, routes compete for limited space, so one small choice can create a contradiction far away. A three-path tile adds slack, making rerouting easier.
Triangles, squares, and hexagons are the regular tessellations of the Euclidean plane. But other surfaces and geometries allow many more possibilities. Different tilings change local flexibility, crowding, and the global complexity of routing.
In two dimensions, paths cannot simply pass through one another. In higher dimensions, extra freedom can remove some bottlenecks and create entirely new kinds of puzzles. Which setups are hardest in each dimension becomes a rich question of its own.
Geometry studies shape and space. Topology studies connection and obstruction. Combinatorics studies arrangement and counting. Path puzzles sit beautifully at the meeting point of all three.
These are not only questions for experts. They are invitations for anyone — students, teachers, puzzle lovers, coders, and researchers — to explore the mathematics hiding inside play.
The real charm of a path puzzle is that it turns simple rules into deep questions. A small tile can control a whole board. A local choice can become a global obstruction. And behind every finished route sits a landscape of unseen mathematical possibilities.
Manage grids, retrieve saved progress, and view solutions.
localStorage.Level 1 - Route the matching letters
All paths perfectly routed.
Configure grid → drag letters to boundaries → save to repository
Design custom routing logic for any geometry.
Drag tiles onto 🗑️ to delete them permanently.