One Line Drawing Puzzle
One Stroke is a classic one-line puzzle with a glowing neon look. Trace every line of the drawing in one continuous stroke, without going over the same line twice. Free in your browser, with a new Daily Challenge every day.
The rules
- Start from any dot and drag to trace the lines.
- You cannot draw the same line twice.
- Lift your finger only when every line is lit. Then the puzzle is solved.
The secret: count the lines at each dot
One-line drawing puzzles go back to a famous problem from 1736. The city of Königsberg had seven bridges, and people wondered whether you could walk across each bridge exactly once. The mathematician Leonhard Euler proved you could not, and in doing so found the rule behind every one-stroke puzzle:
- Count how many lines meet at each dot. A dot with an odd number of lines is an odd dot.
- If there are no odd dots, you can start anywhere and you will finish where you started.
- If there are exactly two odd dots, you must start at one of them and you will finish at the other.
- If there are more than two, the drawing cannot be done in one stroke. Every puzzle in One Stroke has zero or two, so it can always be solved.
More tips
- Leave “bridges”, single lines that connect two parts of the drawing, until last. If you cross one too early, you cannot come back.
- Finish small loops as you pass them rather than leaving them for later.
- If you get stuck, undo a few lines or restart from the other odd dot.
- Three hints per level show you the way when you need them.
Five themed worlds
Early drawings are easy warm-ups, but the shapes soon become clever little mazes where the starting point matters. Levels are generated endlessly, always solvable, and grouped into colorful worlds: Mint Lagoon, Sunset Ink, Neon City, Aurora Sky and Ember Peaks. Calm neon visuals and soft sounds make it a nice puzzle to unwind with.
Daily Challenge
A new puzzle every day, the same for everyone, so you can compare with friends. Enjoy logic puzzles like this? Try the arrow puzzle game Arrow Fling, a pixel art puzzle, or our Sudoku strategies guide.
The simple math behind it
One line puzzles have a neat rule, first found by the mathematician Leonhard Euler in 1736. Count how many lines meet at each point. If every point has an even number of lines, you can start anywhere and you will finish where you began. If exactly two points have an odd number of lines, you must start at one of them and you will end at the other. That one fact solves most of the difficulty: find the odd points first. After that, avoid crossing a bridge, a single line that connects two parts of the drawing, until you have finished everything on your side of it. If you get stuck, restart and try the other odd point. Every drawing in the game can be traced in one stroke, so there is always an answer.
All games on Relax Plays run in the browser on phones, tablets and computers. There is nothing to install and no account to create, and your progress is saved on your device so you can close the tab and come back later.
Frequently asked questions
Is One Stroke free?
Yes. It is free in your browser on phones, tablets and computers.
Is every puzzle solvable?
Yes. Every drawing can be traced in one stroke.
Where should I start?
If two dots have an odd number of lines, start at one of them and you will finish at the other. Otherwise you can start anywhere.