Connect the dots. Fill every cell.
Coloured dot pairs appear on a grid. Connect each pair with a continuous path. Paths cannot cross. Every single cell must be covered. Every puzzle is generated fresh — unlimited, unique, impossible to repeat.
How One Stroke Puzzle works
A grid of cells appears with coloured dot pairs — red dot, red dot somewhere else; blue dot, blue dot; and so on. Your job is to draw a continuous path connecting each pair of same-coloured dots. Drag from any dot and trace a route to its matching partner.
Two rules make this hard. First, paths cannot cross — once a cell is occupied by one colour, no other colour can pass through it. Second, when you finish, every single cell on the grid must be filled. You cannot leave any cell empty. These two rules together mean that the exact route of every path matters for every other path.
Every puzzle is procedurally generated fresh using a Hamiltonian path algorithm that guarantees every cell can be filled and every puzzle has at least one valid solution. The Daily Challenge uses a date seed so every player gets the same puzzle each day. Two modes are on offer: One Stroke Lines gives you several coloured pairs to connect at once, while Color Fill strips it back to a single glowing line that must snake through every cell on the board on its own, start dot to end dot, without ever crossing itself.
Dragging and undoing
Drag from a coloured dot to draw that colour's path. If you go the wrong way, drag backward through your own path to retrace and undo moves. Pressing the Undo button removes the last move. Reset clears the current colour's path so you can start it again.
Why cells must all be filled
This constraint is what makes the puzzle non-trivial. It forces you to plan each path so it fills the "wasted" space, not just the most direct route. The shortest path between two dots almost never fills all the required cells — you have to wind each path through the empty space deliberately.
How to solve it faster
Start with the most constrained pair — two dots that are in a corner or have very few route options. Solving them first limits the space for other pairs in a predictable way.
Think in regions. If a section of the grid can only be reached by one colour, that colour's path must pass through it. Identifying these exclusive zones tells you where each path must go.
Every cell must be filled. If you have connected all pairs but there are empty cells left, at least one path must be rerouted to wind through those cells. Look for which colour is adjacent to the empty area.
Use undo freely. Unlike most puzzles, undoing is not a failure here — it is the expected method. Treat each dead end as information that tells you which direction to try next.
The mathematics behind the puzzle
This type of puzzle sits at the intersection of two mathematical problems. The "connect the pairs" structure is a variant of the disjoint path problem in graph theory, which asks whether K pairs of terminals in a graph can be connected by K mutually non-intersecting paths. On a grid graph, this problem can be verified in polynomial time for small K but becomes NP-complete as K grows — which is why harder versions of the puzzle feel genuinely difficult rather than merely tedious.
The "fill every cell" constraint converts the problem into a variant of the Hamiltonian path problem. The paths together must collectively visit every vertex of the grid exactly once, which is equivalent to partitioning a Hamiltonian path through the entire grid into K segments. This is why the puzzle generator works by constructing a Hamiltonian path first and then dividing it — it guarantees both solvability and complete cell coverage by construction.
The practical result is a puzzle type that scales elegantly with grid size. A 4×4 grid with 3 colour pairs takes most people under a minute. A 7×7 grid with 6 pairs can take five to ten minutes of genuine reasoning. The same mathematical structure underlies both, but the exponential growth in possible path combinations means the difficulty curve is steep.