How to play One Stroke
One Stroke is a one line draw puzzle: every level shows a figure made of dots and lines, and your job is to trace the whole thing in a single continuous stroke. You may pass through a dot as often as you like, but you may never travel along the same line twice, and you cannot lift your pen. It sounds easy until you reach a dead end with three lines still grey.
- Pick a starting dot and press on it with your mouse or finger.
- Drag from dot to dot along the grey lines. Each line you trace turns blue.
- Made a mistake? Drag back along your last line to undo it.
- Turn every line blue before you lift off and the level is complete.
- If you lift off too early the figure resets. Try a different starting dot.
Tips: the secret of one-stroke drawings
- Count the lines at each dot. Every time your stroke passes through a dot it uses two lines: one in, one out. So a dot with an odd number of lines must be where you start or where you finish.
- Two odd dots means a fixed start. If two dots have 3, 5 or 7 lines, begin on one of them. Start anywhere else and the puzzle cannot be finished.
- All even? Start anywhere. When every dot has an even number of lines, any dot works and the stroke ends back where it started.
- Don't burn your bridges. Before you trace a line that is the only link to an untouched part of the figure, finish everything else around you first. Cutting yourself off is the most common way to fail.
- Use the hint. After two failed attempts the odd dots start to glow. That costs you a star but saves a lot of guessing.
The maths behind the puzzle
Drawing a figure without lifting the pen is one of the oldest puzzles in mathematics. In 1736 Leonhard Euler studied the seven bridges of Königsberg and asked whether a walk could cross each bridge exactly once. His answer founded graph theory: a connected figure can be drawn in one stroke only if it has zero or two dots with an odd number of lines. Mathematicians still call such a route an Euler path. Children across Europe know the same idea from the "house of Nikolaus", a little house with a crossed square that you draw in one go, one line for each syllable of a rhyme. You will find that house in level 9.
Knowing the rule tells you where to start, but not which way to go. In the larger figures there are many dead ends, and the real challenge is planning a route that leaves no line stranded. That mix of a simple rule and real planning is what makes one line puzzles so satisfying.
Levels in this game
There are 60 levels. The first ten are classic shapes chosen by hand: a triangle, a square, an envelope, a kite, the house of Nikolaus and a star inside a pentagon, each one introducing a new idea. From level 11 the figures are generated on a dot grid that grows from 3 by 3 up to 5 by 6, with more and more lines and diagonals that cross each other. Each level is created from a fixed seed, so level 37 is the same puzzle for everyone and you can compare notes with friends. Every level is guaranteed to have a solution.
Enjoy brain teasers you solve with a pen? Try Draw Puzzle, where one line and real physics bring two balls together, or test your hand with Draw a Perfect Circle.
One Stroke FAQ
How do you play the One Line Draw Puzzle?
Press on any dot and drag along the lines without lifting your mouse or finger. Each line can only be traced once. Trace every line of the figure in a single stroke and the level is solved. If you lift off early, the lines reset and you can try again from a different dot.
Is every level really solvable?
Yes. The first ten figures were picked by hand to teach the idea, and every later level is built by drawing a random one-stroke path first, so a solution always exists. Our automated tests trace the solution of all 60 levels before each release.
Which dot should I start on?
Count the lines touching each dot. If exactly two dots have an odd number of lines, you must start on one of them and you will finish on the other. If every dot has an even number of lines, you can start anywhere and you will end where you began.
Can I undo a line?
Yes. While you are still holding down, drag back along the line you just traced and it is removed. You can back up as far as you like without starting again.
How do stars work?
Solve a level on your first stroke for three stars, within three tries for two stars, and in any number of tries for one star. After two failed tries the game highlights the dots with an odd number of lines as a hint.
Does it work on phones and is my progress saved?
It works with a finger on phones and tablets and with a mouse or trackpad on a computer. Unlocked levels and stars are saved in your browser on this device, with no account and no download needed.