One Line

One Line is a tracing puzzle. A small drawing made of dots and lines appears on the screen, and your task is to draw all of it in a single stroke, never lifting your finger and never going over a line twice.

How to play

The goal is to draw every line of the picture exactly once.

• Starting: touch a dot and drag along a line to the next dot. You can also tap the dots one after another instead of dragging.
• Every line once: a line you have drawn is used up. You cannot draw over it again.
• Dots as often as you like: you may pass through the same dot many times, as long as you always arrive on a line you have not used.
• Lines run in several directions: sideways, up and down, and diagonally from corner to corner of a square.
• Winning: when every line has been drawn, you win.

If you take a wrong turn, drag back along the line you just drew, or press Undo. On a computer, the Backspace key also takes a step back. Some pictures can only be started at certain dots. If a dot will not let you start, try another one.

The Hint button names the next line to draw. It is unlimited on the early levels and limited on the later ones.

The levels

The levels change the size of the picture and the number of lines. Each picture sits on a lattice of dots, which is 4 dots wide on Easy and 7 on Expert.

• Easy: a small picture of 8 to 12 lines.
• Medium: 14 to 20 lines. A few wrong turns hide in it.
• Hard: 22 to 30 lines. Plan your path first. You have 5 hints.
• Expert: 32 to 40 lines, and only two dots can start it, so choosing the right start matters. You have 3 hints.

The pictures are not random. For each level, a computer made many candidates and kept those that a simple pencil follower, one that never looks ahead, got wrong most often. So the hard and expert pictures are the ones with the most dead ends. Each picture may also be turned or flipped when it is shown to you.

Today's game

The daily game is a Medium picture. Everyone who plays on the same calendar day gets the same one.

Tips

1. Count the lines that meet at each dot. A dot with an odd number of lines must be where you start or where you finish.
2. If every dot has an even number of lines, you can start anywhere, and you will end where you began.
3. If exactly two dots have an odd number, start at one of them. You will finish at the other.
4. A dot with only one line on it must be the start or the end of your stroke, because you could never leave it again.
5. Every time you arrive at a dot you need a fresh line to leave by, except at the very end. Do not use up all the lines around a dot too soon.
6. Before you start, trace the picture with your eyes once. Looking for loops and branches shows you the shape of the route.
7. Use your hints on Hard and Expert only when you are sure you are stuck. They are limited.

A bit of history

The idea behind this puzzle is very old. In the 1700s the mathematician Leonhard Euler asked the same question about the bridges of a town, and his answer is why we count the odd dots today.

Questions

Why can't I start from this dot? For some pictures, a full stroke is only possible from certain dots. The game only lets you start where one can work.

Can I cross the same dot twice? Yes. A dot can be visited many times. Only the lines are used up.

Is every picture solvable? Yes. Each one is built so that a one-stroke route exists, so a perfect route is always there to find.

What does Undo do? It takes back your last line. You can use it as many times as you like.