Slitherlink puzzles

What it is

From a grid of dots and scattered numbers, you draw a single unbroken loop that winds through the grid without ever crossing or branching, guided only by clues telling you how many of each cell's four sides the loop must use. Slitherlink is a logic puzzle in which you connect dots with line segments to form one continuous loop, satisfying numeric clues that specify how many edges surround certain cells. It is an elegant, purely deductive puzzle with no arithmetic, prized for the satisfying way a single closed loop emerges from simple local clues.

The rules are spare and beautiful. The grid is a lattice of dots, and you draw horizontal or vertical segments between adjacent dots to build one single closed loop. Numbers inside cells tell you exactly how many of that cell's four edges are part of the loop, a "3" means three of its sides are used, a "0" means none. The loop must be a single continuous circuit with no crossings, no branches, and no separate loops, which is the constraint that ties everything together.

The deduction it produces is wonderfully intricate. A "0" clue forbids all four surrounding edges, a "3" next to a "0" creates forced segments, and corners and adjacent clues interact in ways that let you steadily deduce where the loop must and must not go. The single-loop rule adds a global constraint, since you can rule out any move that would close a small loop early or create a dead end, and skilled solvers learn a repertoire of recurring patterns.

It costs little, found in puzzle books and free apps, needs only a pencil, and suits anyone who loves pure logical deduction without numbers to add. The combination of minimal rules, deeply satisfying loop-building, and the clever interplay of local clues and the single-loop constraint makes Slitherlink puzzles an absorbing and elegant mind-at-play pursuit.

How it works

Learn the rules and grasp what the numbers mean, because Slitherlink's loop logic is unlike grid-filling puzzles. You draw segments between adjacent dots to form a single closed loop, and each number tells you exactly how many of that cell's four sides the loop uses, from zero to three. The loop must be one continuous circuit with no crossings, branches, or separate loops. Start with a small, easy puzzle in a book or app, and use a notation for edges you have ruled out as well as those you have drawn.

Start from the most informative clues. A "0" is gold, since it forbids all four of its cell's edges immediately, and a "3" forces three edges, so look for these and for clues sitting next to each other or in corners, which often force segments. Marking ruled-out edges with a small cross is as important as drawing confirmed segments, because knowing where the loop cannot go drives much of the deduction. Work outward from these certainties as they constrain neighbouring cells.

Use patterns and the single-loop rule to finish. As you progress, recurring local patterns, such as two adjacent "3"s, force known arrangements you will come to recognise on sight, speeding things up. The single-loop constraint lets you reject any segment that would close a small loop prematurely or strand a dead end, which resolves many otherwise ambiguous spots. Keep alternating between local clue deductions and this global rule. With patience the unique loop emerges, so guessing is never needed.

Mark edges you have ruled out, not just those you draw, since tracking where the loop cannot go is as essential to the deduction as tracking where it does.

Benefits

Elegant Single-Loop Logic Pure Deduction, No Arithmetic Satisfying Pattern Recognition Difficulty Scales Widely A Refreshing Change From Grids Screen-Free on Paper Cheap or Free to Play

What you need

Here's what to gather before you start. The essentials are marked.

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Slitherlink puzzles: from books or apps

A pencil: to draw segments and mark crosses

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Pencil

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An eraser: since deduction involves corrections

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Eraser

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The core rules: clue counts and a single closed loop

A crossing-out notation: for forbidden edges

A quiet moment: to concentrate on the deduction

Patience: to learn the recurring patterns

FAQs

What is the goal of Slitherlink?

To draw a single continuous loop through a grid of dots, guided by numeric clues. You connect adjacent dots with horizontal or vertical segments to form one closed loop, and the numbers inside cells tell you exactly how many of that cell's four sides the loop uses. The loop must be a single circuit with no crossings, no branches, and no separate loops. So you are deducing the unique path of one winding closed loop that satisfies every clue, which produces an elegant, purely logical puzzle with no arithmetic involved.

Is there any maths in it?

None beyond reading small numbers. The clues simply state how many of a cell's four edges the loop uses, from zero to three, so there is no addition or calculation, only counting and pure logical deduction. This makes Slitherlink appealing to people who enjoy logic puzzles but prefer to avoid the arithmetic of puzzles like Kakuro or KenKen. The entire challenge lies in reasoning out where the loop must and must not go from the local clues and the global single-loop rule, which is what gives the puzzle its elegant character.

How do I start a puzzle?

Begin with the most informative clues, especially "0" and "3". A "0" immediately forbids all four edges around its cell, and a "3" forces three of its edges, so these, along with adjacent clues and corners, create forced segments to start from. Just as important is marking edges you have ruled out with a small cross, since knowing where the loop cannot go drives much of the deduction. Work outward from these certainties, letting them constrain neighbouring cells, and the loop's path gradually emerges.

Why do experienced solvers seem so fast?

They recognise recurring patterns. Slitherlink contains many local configurations that always force the same arrangement of edges, such as two adjacent "3" clues, and skilled solvers learn this repertoire so they can place segments on sight rather than deducing afresh each time. Much of advanced solving becomes pattern recognition layered on the basic logic. Combined with diligent marking of forbidden edges and use of the single-loop rule to reject premature small loops, this pattern knowledge is what lets practised solvers move through even large grids quickly.