How to play One Stroke

A puzzle for one: a figure of dots and lines, to be drawn in one stroke without lifting your finger.

Players: 1
What you need: A figure of dots and lines, 9 to 42 lines
How long: Under a minute to a few minutes a figure

What One Stroke is

One Stroke is a puzzle for one. The page shows a figure, dots joined by grey lines. The aim is to draw over every line in a single stroke, the way a child draws a house without lifting the pencil.

A line can be drawn only once. The stroke runs from dot to dot, and it can pass through a dot as often as it likes, but never along a line it has already drawn.

A house of eight lines, three of them drawn. The stroke is at the top of the roof, and the left side of the roof is next.

Playing it here

Touch a dot to start the stroke there.
Drag your finger along the grey lines from dot to dot. Each line you pass over is inked in colour. Tapping the next dot works too.
Keep going until every line is inked.

Going back along the line you just drew takes it back, and so does Undo. Start again lifts the whole stroke. Hint shows where to go. On a computer, U takes a line back and H asks for a hint.

Where to start

Count the lines at each dot. A stroke that passes through a dot uses two of its lines, one in and one out, so a dot with an odd number of lines has to be where the stroke starts or where it ends. A figure with two such dots can only be drawn from one of them to the other.

When every dot has an even number of lines, start anywhere: the stroke will end where it began. Every figure here has either no odd dots or exactly two.

Three lines meet at each eave and two at every other dot. So the stroke has to start at one eave and end at the other.

Do not strand yourself

Starting at the right dot is not always enough. If the stroke finishes one part of the figure while lines elsewhere still need it, it can end up somewhere with no line left to take.

The rule that saves you: do not cross a line that is the only way back to lines still waiting, unless there is nothing else to take. If you do get stuck, go back along your stroke or press Undo. It costs nothing but time.

Down the tail first, and the stroke is stranded at the bottom with the whole diamond still to draw. Round the diamond first, then down the tail.

Lines drawn twice

With the setting on, some lines are doubled, drawn as two thin lines side by side. A doubled line has to be drawn twice, once each way or twice the same way, and each pass inks one of the two. When counting the lines at a dot, a doubled line counts as two.

A doubled tail, drawn once. One more pass down or up it, and it is done.

How a figure ends

The figure is drawn the moment the last line is inked. The clock stops there, and your time is kept as your best at that level if you took no hint. Steps back do not count against you: the clock has already charged for them.

Every figure here can be drawn. It is made by drawing it: half a figure is walked on one side of the middle and mirrored onto the other, which is why the figures are symmetric, and the walk itself is a way to draw it.

Today’s figure

Each level has a figure of the day, the same for everybody in Nepal, which changes at midnight in Kathmandu. Draw it as often as you like: your best time on it is kept.

A new figure is made fresh every time, as many as you like.

A few tips

Before you touch anything, look for the dots where an odd number of lines meet. If there are two, start at one of them.
Leave the tails and loose ends for last, unless one of them is where you have to start.
When the stroke reaches a dot with several lines left, take one that keeps the rest of the figure in reach.
Stuck? Going back one or two lines is usually enough. Hint tells you exactly how far.

Settings

One Stroke has two settings, and the page asks first whether you want today’s figure or a new one.

Setting	Standard	What it changes
Figure	Easy, about a dozen lines	How big the figure is, from about a dozen lines to forty. A bigger figure has more places to strand yourself.
Lines drawn twice	None	Whether some lines are doubled and have to be drawn twice. It changes which dots are odd, so a figure has to be read again.

Words

Stroke: The one line your finger draws, from where it starts to where it ends, without lifting.
Dot: A point of the figure where lines meet. The stroke may pass through a dot as often as it likes.
Odd dot: A dot with an odd number of lines. A stroke must start or end at one.
Doubled line: A line drawn as two thin lines side by side, which has to be drawn twice.

Every rule on this page is the one the app plays by. Change any of them on the game's own page before you start.