Why lines get left over
Imagine each line disappears once you draw it. If at some moment the remaining lines split into two separate groups, you can finish the group you are in, but there is no way across to the other one. Almost every leftover-line failure is this.
Bridges last
A line whose removal would split the remaining figure in two is called a bridge. The method Fleury described in 1883 fits in one sentence:
“If you can choose another line, do not cross a bridge.”
| Lines available from your dot | What to do |
|---|---|
| At least one non-bridge | Take it |
| Only one, and it is a bridge | Cross it (the only time you should) |
| Only several bridges | You are already stuck; go back |
As long as your start is right, following this rule always gets you to the end.
Choosing at a fork
- Clear dead-end branches first: small loops or tails attached on one side are best done while you are next to them.
- Save the lines into your finish: on a 2-odd-dot board, keep the lines leading into the finishing dot for last.
- Watch degree-2 dots: once you pass through a dot with only two lines, it is used up. Make sure the lines beyond it are not cut off.
- Leave busy hubs for later: dots where many lines meet can be visited several times, so they make good connectors to keep in reserve.
When you are stuck
Rather than restarting, go back to the last point where you crossed a bridge and pick another line. On large boards this saves a lot of time.
In the app
Drag back to erase
In OneTrail, dragging back along the way you came erases the last line. The Undo button removes one line at a time and Restart clears the board.
Dead-end warning and blocking
With Warn on dead ends on, the game tells you the moment the puzzle can no longer be finished. Beginners can also turn on Block dead-end moves, which refuses any move that would make the puzzle unsolvable. In effect, the app enforces the bridge rule for you.
Hints that rewind
Before you start, a Hint shows a valid starting dot; mid-puzzle, it points to a line that still lets you finish. If you are already stuck, it rewinds you to the last moment the puzzle was still solvable. Hints refill to 3 each day, a short video gives 3 more, and when no video is available you get them anyway.
FAQ
How do I spot a bridge?
Cover the line with your finger and look at the lines you have not drawn yet. If they fall into two separate groups, it is a bridge.
Do hints show up in my records?
Your clear record stores how many hints you used. A solve with no undos and no hints is counted separately as a perfect solve.
OneTrail: One Line Draw Puzzle
No sign-up, fully offline, and every board is checked to be solvable before you see it. Free on Android.