🧩 One Stroke
Puzzle / Logic · Free online · No download · No sign-up
One Stroke gives you a grid of cells and asks you to draw a single continuous path that passes through every cell exactly once. You cannot lift your finger — the path must be unbroken from start to finish. Simple grids of five or six cells are solvable by trial and error. Larger grids of twenty or more cells require genuine spatial planning: you must mentally trace possible routes before committing to any, because a wrong early turn can permanently block the path from reaching certain cells later.
How to play One Stroke
- Tap the starting cell to begin your path — it is marked with a dot or highlighted border.
- Drag through adjacent cells (up, down, left, right — no diagonals) to draw your path.
- The path must visit every cell on the grid exactly once.
- You cannot cross or revisit cells you have already drawn through.
- If you reach a dead end before visiting all cells, lift and tap the starting cell to reset.
- Complete the path to the marked end cell to solve the puzzle.
Tips to beat your high score
- Identify forced cells first. A cell that is surrounded on three sides (by walls or grid edges) can only be entered and exited in one direction. These cells constrain the path completely — resolve them before planning the rest of the route.
- Plan the last few cells carefully. The end of the path is the most constrained section — you need to arrive at the final cell from exactly the right direction. Work backwards from the end cell to see what approach direction is required.
- Avoid creating peninsulas. A peninsula is a group of unvisited cells that can only be accessed through one adjacent cell. If you draw your path in a way that isolates a group of cells, you will never be able to visit them. Scan for peninsulas forming as you draw.
- Prefer paths that hug edges early. Running the path along the outer border first preserves the interior as open space, reducing the risk of splitting the remaining cells into isolated regions.
- Reset often and reset early. Sunk-cost thinking causes players to persist with a flawed path long after the dead end is inevitable. The moment you see that a section of cells is going to be unreachable, reset immediately rather than finishing the current wrong path.
What this game trains your brain to do
One Stroke is a direct implementation of the Hamiltonian path problem — the mathematical question of whether a graph contains a path that visits every vertex exactly once. Unlike its cousin the Euler path (which must traverse every edge), the Hamiltonian path problem is NP-complete: no polynomial-time algorithm is known for the general case, which means it cannot be mechanically solved by brute-force search at the scale humans encounter it. Instead, human solvers use spatial heuristics, constraint propagation, and mental simulation — sophisticated reasoning tools that the puzzle sharpens with each attempt.
The cognitive demands of One Stroke centre on spatial planning and prospective memory: keeping track of the constraint that you have not yet visited certain cells while simultaneously planning how to reach them without being blocked. The prefrontal cortex governs this planning function, and research on planning games shows that regular practice produces measurable improvements on unrelated spatial reasoning tasks, including maze navigation, route planning, and structural design problems.
About One Stroke
One Stroke is inspired by the class of pencil puzzles known as Hamiltonians or number mazes, which have appeared in puzzle books since the 19th century when Sir William Hamilton studied the mathematics of graph paths. CrizBrain’s version generates grids of increasing size and complexity, providing a fresh spatial challenge every session without repeating solutions.
All CrizBrain games run entirely in your browser with no account and no data sharing. Your best puzzle completion count is saved locally on your device. One Stroke takes seconds to understand and provides a satisfying “aha!” moment every time a tricky grid finally clicks into a clean path.