Beamstroke One-Line Puzzle
Draw a single line from the glowing ring so that it passes through every open cell exactly once. The line moves up, down, left or right, never diagonally. Seven lessons teach the rules, and after that you can move on to generated levels and a new board each day.
💡 About This Tool
Four kinds of special cell appear on the boards.
| Cell | Looks like | Rule |
|---|---|---|
| Insulator block | Black stripes | Cannot be entered |
| Relay gate | Numbered hexagon | Pass in number order |
| One-way prism | Arrow | Leave only along the arrow |
| Receiver | Double circle | The line must stop here |
The lessons run from 3×3 to 6×6, with target times from 20 to 110 seconds, and you can play them in any order.
In Levels, clearing a board opens the next one. Boards grow like this:
| Level | Board | What is added |
|---|---|---|
| 1-3 | 5×5 | Insulator blocks |
| 4-6 | 5×6 | 2 gates |
| 7-10 | 6×6 | 1 arrow |
| 11-15 | 6×7 | 3 gates, receiver |
| 16-20 | 7×7 | 2 arrows |
| 21-30 | 7×8 | More blocks |
| 31-40 | 8×8 | 4 gates, 3 arrows |
| 41-60 | 8×9 | More blocks |
| 61+ | 9×9 | 4 arrows |
The Daily board is 7×7 and is set by the date, so on the same day every device gets the same puzzle.
You start with three stars. Using any hint costs one, using three or more costs another, and going past the target time costs one more. You always keep at least one. In Levels, the target time is 10 seconds plus 1.5 seconds per open cell.
🧐 FAQ
Q. Can a board be impossible? No. Generated boards are made by building a correct path first and turning it into a puzzle. There can be more than one answer, and any path that follows the rules counts.
Q. How do I fix a mistake? Trace the line backwards to erase it. Tapping a cell in the middle of the line removes everything after it. The Undo and Restart buttons also work.
Q. When does the clock start? On your first move. It stops while you are on another tab and while the board is scrolled off the screen.
Q. Why did Hint move my line back? If the current line cannot reach a finished board, Hint moves it back to the point where it matches the answer and lights up the next cell.
Q. Can I move my records to another device? Yes. Export a save code in the Stats & settings tab, paste it on the other device and press Import.
📚 Fun Facts
A board game that sold badly gave this puzzle its name
Visiting every cell once is known in mathematics as a Hamiltonian path, after the Irish mathematician William Rowan Hamilton. In 1857 he showed a game at a meeting in Dublin: follow the edges of a dodecahedron and visit all 20 corners exactly once. A London game maker, Jaques and Son, began selling it in 1859 under names such as Around the World. It did not sell well.
The name did last. It is often set beside the Eulerian path, which uses every line once instead of every point. Euler's version has a simple counting test. Hamilton's has no such shortcut known, which is part of why a Beamstroke board can look easy and still take a while.