Slitherlink Rules: How to Play, Patterns and Strategies

What is Slitherlink?

Slitherlink is a loop-drawing logic puzzle from Japan. You start with a rectangular lattice of dots, and some of the squares between the dots contain a number from 0 to 3. Your task is to join neighboring dots with horizontal and vertical lines so that they form one single closed loop, with no branches, no crossings and no loose ends.

The numbers are the only clues. Each one tells you how many of that square's four sides are part of the loop. A 0 means none of them, a 3 means all but one. Squares without a number can have any number of sides on the loop.

The puzzle is also sold as Fences, Takegaki, Loop the Loop and Loopy, among other names. Whatever the label, the goal is the same: find the one loop that satisfies every clue. Slitherlink is a favorite among experienced solvers because its tiny rule set produces a remarkable variety of patterns, and the moment the loop finally closes is one of the most satisfying in puzzling.

A short history

Slitherlink is an original puzzle of Nikoli, the Japanese publisher behind many of the best-known pencil puzzles. It first appeared in Puzzle Communication Nikoli issue 26 in June 1989. According to the Wikipedia article on Slitherlink, the editor combined two puzzles sent in by readers, and in its earliest form every square carried a number and the lines did not have to form a loop.

The single-loop rule turned it into the puzzle known today, and it has sat alongside Sudoku, Hashiwokakero and Nurikabe in Nikoli's catalog ever since. You can see the publisher's own introduction on Nikoli's English Slitherlink page.

It also made an early jump to video games. Bandai released a Slither Link game in Japan for the WonderSwan handheld in 2000, and Hudson Soft released a Slitherlink title for the Nintendo DS in Japan in 2006. Today it is a staple of puzzle books and apps worldwide.

The rules of Slitherlink

Slitherlink has five rules:

1. 1Connect neighboring dotsDraw lines only between dots that sit next to each other horizontally or vertically. Diagonal lines are not allowed.
2. 2Make one loopAll the lines together must form a single closed loop. A second, separate loop anywhere in the grid breaks the rules.
3. 3No branches or crossingsThe loop never splits, crosses or touches itself. At every dot, either exactly two lines meet or none do.
4. 4Numbers count sidesA number inside a square tells you exactly how many of that square's four sides are part of the loop.
5. 5Blank squares are freeA square without a number has no clue of its own. Its sides are decided entirely by the rest of the puzzle.

The loop does not have to visit every dot, and it may run along the outer border of the grid. A well-made Slitherlink has exactly one solution, reachable by logic alone.

A worked example

This 5×5 puzzle has just eight clues. The solution on the right shades the area inside the loop, which makes it easy to check each number.

Check a few clues against the answer. The 3 has its top, left and right sides on the loop, with only the bottom side open. Both 0s sit in open territory with no loop lines around them. The 1 on the left edge touches the loop only along its left side, which is the border of the grid, because its other three neighbors are inside the loop with it. That last point is worth remembering: the outer edge of the grid is a perfectly legal place for the loop to run.

How to play: a step-by-step method

Mark lines you are sure of, and put a small x on sides you know are empty. Then work through this routine:

1. Cross out around every 0. None of the four sides of a 0 can be on the loop. Mark each one with an x so you remember it is closed.
2. Work the 3s next. A 3 has only one side missing. Any side you can rule out forces the other three onto the loop.
3. Apply the dot rule everywhere. Every dot has exactly zero or two lines. If a dot has one line and only one open direction left, the loop must continue that way. If it already has two lines, cross out the rest.
4. Crack the corners. In a corner of the grid, a 1 can never use the two outer sides, and a 3 must use both of them. Both facts come straight from the dot rule at the corner dot.
5. Extend every loose end. Each line segment must eventually join the rest of the loop. Follow loose ends and see where they are forced to go.
6. Never close a loop early. If joining two line ends would close a loop while other segments are still unconnected, that gap must stay open.

Patterns and strategies

Experienced solvers rarely reason from scratch. They recognize a set of standard patterns and fill them in on sight. These are the ones to learn first.

Patterns like these are easiest to learn by repetition, so pick a small grid and solve a few in a row. The Slitherlink games on LogicPuzzles.io start at 5×5 and go up to 10×10, with a fresh 7×7 every day.

Variations and relatives

The same rules work on many kinds of grid, and several related puzzles share Slitherlink's line-drawing spirit:

• Other tilings. Slitherlink can be played on hexagons, triangles and more exotic tilings, including Penrose and Laves patterns. The rules stay the same, but cells with more sides allow higher numbers and more possible paths from each dot.
• Bigger grids. Puzzles range from 5×5 warm-ups to large rectangles with hundreds of squares. Size alone does not make a puzzle hard; sparse clues and few 0s and 3s do.
• Masyu. Masyu also asks for a single loop, but its clues are black and white circles that tell the loop where to turn or go straight.
• Hashi. Hashiwokakero draws lines too, but builds a connected network of bridges between numbered islands instead of a loop.

Common mistakes to avoid

Most stuck positions in Slitherlink trace back to one of these habits:

• Leaving a dead end. A dot with exactly one line is never finished. If you cannot see where a line goes next, the dot rule usually tells you.
• Closing a small loop. A neat little loop that satisfies nearby clues is wrong if other lines are left outside it. The solution is always one loop.
• Avoiding the border. Beginners often assume the loop stays away from the outer edge. It can run along the border, and many clues near the edge depend on it.
• Not marking empty sides. Crossing out sides you know are empty is as important as drawing lines. Without those x marks, the dot rule and the number clues are much harder to apply.
• Counting the wrong square. Each line is a side of two squares. After drawing one, check the clues on both sides of it.

What makes Slitherlink hard

Easy Slitherlink puzzles are full of 0s and 3s, and the standard patterns resolve most of the grid. Medium puzzles lean more on 1s and 2s, which constrain far less on their own, so you spend more time applying the dot rule and following loose ends. Hard puzzles add long-range reasoning: the loop has to reach distant parts of the grid without closing early, and inside and outside coloring becomes essential.

Mathematicians have shown that solving Slitherlink in general is NP-complete, so there is no known shortcut that works on every possible grid. Published puzzles are built to be solved by logic, though, and every step can be justified without guessing.

If you enjoy Slitherlink, you will probably like Masyu and Nurikabe, which reward the same mix of local patterns and whole-grid thinking.

Frequently asked questions