Puzzle guide

How to solve Slitherlink

In Slitherlink you draw one long loop through a field of dots. The numbers tell you how many sides of each cell the loop touches. A few small patterns open almost every board, and once you know them, the loop seems to draw itself. Here they are, with pictures.

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The rules

Join the dots with lines to make one loop. It ends where it started.
A number tells you how many sides of its cell the loop runs along. A cell without a number can have any number of lines.
The loop never splits and never crosses itself. Every dot has two lines or none.

A solved puzzle

A solved puzzle: one closed loop. Count the lines around each number: the 3s have three, the 1s have one.

Your first moves

Find every 0 and put an X on its four sides. No line can go there.
Look at the corners of the board. A 3 in a corner gives you two lines right away.
Follow every line you draw. At each dot it has to go on somewhere, and often there is only one way left.
Put an X on every edge you know is empty. The X marks are what force the next lines.

Techniques, step by step

A 0 shuts all four sides

A 0 means the loop touches none of the four sides of that cell. Put an X on all four. That sounds small, but those X marks reach into the neighbouring cells: the numbers next to a 0 have fewer edges left to choose from.

The 0 gets four X marks.

A 3 in a corner

A 3 in a corner of the board must use both of its outer sides. If it left one out, it would have to use the other three, and the line would end at the corner dot with nowhere to go. So draw the top and the left side straight away. The same trick works for a 1 in a corner, the other way round: both outer sides get an X.

The corner 3 always takes its two outer sides.

A line never stops at a dot

Every dot has two lines or none. Here a line arrives at the middle dot, and two of its other edges already have an X. The line cannot stop, so it must go on along the only edge that is left: down. It works the other way too: a dot with an X on every edge but one gets an X on that one as well, because a line there would be a dead end.

Two ways are blocked, so the line goes down.

A 3 next to a 0

The 0 shuts its side towards the 3, so the 3 has to use its other three sides. And the lines keep going: at the two dots next to the 0, the line cannot turn into the 0, so it runs on up and down. One pair of numbers gives you five lines at once. Two 3s side by side are another pattern worth knowing: the edge between them and their two outer sides are always lines.

The 3 takes its three free sides, and the lines run on past the 0.

Do not close the loop too early

There is only one loop. If joining two line ends would close a small loop while other lines are still somewhere else on the board, that edge is wrong. Put an X on it. This is the idea almost every bigger board needs, often more than once, so whenever two ends come close, ask: would this close the loop before everything is joined?

Closing the gap would make a loop on its own. It gets an X.

Inside and outside

The loop splits the board into two parts: inside and outside. Every cell belongs to one of them, and everything beyond the edge of the board is outside. A line runs between two cells exactly when one is inside and the other is outside. So if you know two neighbouring cells are on the same side, the edge between them gets an X, and if they are on different sides, it is a line. On hard boards, colouring cells in your head as in or out finds the steps the patterns miss.

Common mistakes

Making two loops. The board is solved only when all the lines form one single loop.
Counting the wrong cell. A number counts the four sides of its own cell, not the lines near it.
Leaving line ends open. Every line end must go on. A dot with exactly one line is never finished.
Forgetting the X marks. Most lines are found because the other edges at a dot are already ruled out. Mark them.

Questions and answers

What is Slitherlink?

A logic puzzle where you draw one closed loop along the lines between dots. Numbers in the cells tell you how many of their four sides the loop uses. It is also called Loop the Loop or Fences.

Can the loop cross itself or split?

No. It is one simple loop: every dot has exactly two lines or none.

What does an empty cell mean?

Nothing: a cell without a number can have zero, one, two or three of its sides on the loop.

Where do I start?

Put X marks around every 0, then look for 3s in corners and 3s next to 0s. From there, follow the lines you drew dot by dot.

What is the hardest part?

Remembering that there is only one loop. On big boards the step you are missing is often an edge that would close a loop too early, so it must stay empty.

Ready to play?

Shut the 0s, take the corners, follow every line and never close the loop too early. That is how a Slitherlink falls, from the small boards to the big expert ones.