One-Stroke Puzzle
Trace every line exactly once. Each puzzle is generated automatically, so there is always a new one to try.
How to play
- Pick any dot to start by tapping it with your finger or pressing it with the mouse.
- Move to a neighboring dot along a line. Either drag along the line, or tap the next dot in turn.
- Lines you have used change color. You cannot use the same line twice, but you can pass through a dot as many times as you like.
- When every line has been used, you solve the puzzle.
If you get stuck, press Undo to step back one line at a time, or Reset to start the puzzle over.
Buttons
- Undo: Goes back one line. If you have only picked a starting dot, it clears that choice.
- Reset: Restarts the same puzzle.
- Hint: Shows which dots you can start from, with dotted circles.
- New puzzle: Generates a different drawing.
- Answer: Shows one possible drawing order as numbers on the lines.
- Warn me about dead ends: When on, the game tells you right away about moves that leave you stuck, and about starting dots from which you cannot finish.
Difficulty
| Easy | 5 dots, 6 to 8 lines |
|---|---|
| Normal | 7 dots, 9 to 12 lines |
| Hard | 9 dots, 13 to 17 lines |
| Insane | 12 dots, 19 to 24 lines |
Your best (fastest) time for each level is saved in your browser only, and is not sent to any server.
When is a one-stroke drawing possible?
Whether a figure can be drawn in one stroke depends on its number of "odd dots", meaning dots where an odd number of lines meet.
- 0 odd dots: You can start from any dot. You will end up back where you started.
- 2 odd dots: Start at one of them and you will finish at the other. Starting from any other dot, you cannot finish.
- 4 or more odd dots: A one-stroke drawing is impossible. The number of odd dots is always even.
Every figure in this game is built so that it can be drawn in one stroke. The dotted circles shown by the Hint button are these odd dots.
This idea comes from the 18th-century mathematician Leonhard Euler, who worked it out while solving the Seven Bridges of Königsberg problem: could you walk through the city crossing each of its seven bridges exactly once?
Tips
- Find the odd dots first. With two odd dots, your starting point is down to two choices.
- Save dead-end lines for last. Lines you cannot come back from should come late in your route.
- Finish nearby loops in one go. Do not leave a loop behind in the middle of your route.
- When in doubt, Undo. You can go back as often as you like, so experiment freely.