How to play one line puzzle
- Look at the figure. Dots sit on a wooden board; untraced lines are dark walnut. This page ships 18 hand-built figures — from a short line to bridges and twin triangles.
- Start on a glowing peg. Legal starting pegs glow. Figures with two odd-degree corners must start (and end) on those corners; closed loops can start on any peg that has a line.
- Trace every line once. Keep tapping a neighbour along an unused line. You may not lift the stroke or reuse a line. The counter shows how many lines you have covered.
- Use Undo, Reset or Hint. Undo removes the last segment. Reset clears the level. Hint plays one step from an Euler-path solution (Hierholzer). Games that used Hint do not update your best.
One stroke strategy
- Count odd corners first: if there are two, you must start on one of them.
- Save bridges (lines whose removal would split the remaining figure) for later — Hint follows the same idea.
- If you paint yourself into a dead end, Undo a few segments instead of Reset; most early mistakes are local.
- Closed loops (no odd corners) can start anywhere; pick a peg that keeps options open.
Why every level is solvable (Euler paths)
A connected figure has a one-stroke route exactly when it has zero or two odd-degree dots — Euler’s theorem for paths. We build each of the 18 boards by hand and verify an Euler path with Hierholzer’s algorithm at build time. The sample House board needs 6 line traces in one particular solution.
Hint uses the same path finder on whatever lines are left, so following Hint always finishes a solvable board.
More logic puzzles
Like planning a route? Try Lights Out, Dots and Boxes, peg solitaire or Tower of Hanoi. Chinese speakers can play the 一笔画 version of this page with the same saved progress.