One-Stroke Puzzle (Drag or Tap, with Hints)
Trace every line of the figure in a single stroke, without lifting the pen or going over a line twice. Every puzzle is guaranteed to be solvable, so if you hit a dead end, you just took the wrong route. Undo and hints are there when you need them. For another puzzle, try Sokoban.
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- Lines drawn
- 0 / 0
- Odd dots
- 0
Pick the dot where you want to start.
How to use
- Choose a "Difficulty" (changing it gives you a new puzzle).
- Click or tap the dot where you want to start, then drag to a connected dot, or tap the dots one after another.
- You cannot reuse a line. Cover every line to win.
- If you get stuck, use "Undo" or "Hint". "Reset" starts the same puzzle again and "New puzzle" gives you a different figure.
Notes
- Every figure is generated so that a one-stroke path exists: it is connected and has either 0 or 2 odd dots.
- With 2 odd dots you must start at one of them. With 0 odd dots you can start anywhere and you will end where you began.
- Places where lines cross are not dots, so you cannot turn there. Corners exist only at the circles.
- "Hint" shows a next move that still lets you finish, avoiding bridges that would strand you. Hints are not tracked.
- The puzzle and your progress are kept only while this page is open; nothing is saved or sent anywhere.
Glossary
One-stroke path (Eulerian trail)
A route that uses every edge exactly once. It exists only when the figure is connected and has 0 or 2 odd vertices (Euler’s theorem).
Odd vertex
A vertex where an odd number of lines meet. With 2 odd vertices you start at one and finish at the other; with none you finish where you started.
Bridge
A line that cuts you off from the part you left once you cross it. While another choice exists, keep the bridge for last (Fleury’s algorithm).
FAQ
How can I tell whether a figure can be drawn in one stroke?
It must be connected and have either 0 or 2 odd vertices (vertices where an odd number of lines meet), according to Euler’s theorem. Every puzzle here is generated to meet that condition.
What should I do if I reach a dead end?
Use "Undo" to take back the last line. If the figure has 2 odd dots you must start at one of them, so try "Reset" and begin from a different dot.
How does the hint choose the next move?
It checks that the remaining lines can still be covered in one stroke after the move, and only suggests such moves. Bridges that would strand you are avoided while another choice exists, in the spirit of Fleury’s algorithm.
Can I play without dragging?
Yes. You can click or tap the dots one after another. With a keyboard, focus a dot and press Enter or Space.
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