How to Solve Slitherlink: Corner Rules and the Loop Constraint

Updated August 2026

Slitherlink gives you a grid of dots and a scattering of numbers, and asks for one closed loop that never crosses or branches. Beginners stall because they try to reason about the whole loop at once. Strong solvers do the opposite: they work tiny local patterns around each clue, mark edges as definitely-on or definitely-off, and let the single-loop rule finish the job.

The rules, stated precisely

• Draw line segments between adjacent dots to form exactly one closed loop.
• The loop never branches and never crosses itself, so every dot has either zero or exactly two segments touching it.
• A number in a cell says exactly how many of that cell's four sides are part of the loop. Cells with no number are unconstrained.

That "zero or two" condition at each dot is the engine of the whole puzzle, and it is the thing new solvers underuse. Marking edges you have ruled out is just as productive as drawing edges you have ruled in.

Start with 0s and 3s

A 0 is a gift: all four of its sides are off. Cross them out immediately. The effect spreads, because a neighbouring clue has just lost one of its options.

A 3 is the other extreme — three of its four sides are on, so at most one is off. Two 3s that share an edge force that shared edge on, plus the two outer edges parallel to it. Two 3s sitting diagonally are the single most useful pattern in the game: the two outer corners of the pair are always on. Learn that shape and you will spot it on almost every board.

A 1 in a corner of the grid has both of its outside edges off, because turning either on would force the loop into the corner dot with nowhere to go. A 3 in a corner has both outside edges on for the mirror-image reason.

Work the dots, not just the cells

Every time you draw a segment, walk to both of its dots and ask what they now permit. A dot with one segment attached needs exactly one more, so if three of its four directions are crossed out, the fourth is forced. A dot with two segments is finished — cross out its remaining directions at once. This dot bookkeeping is where most of the progress on a hard board actually comes from, and it costs nothing but attention.

Dead ends are illegal, and that is a tool

A segment that leads to a dot with no legal continuation cannot exist. So whenever you are unsure about an edge, follow it: if drawing it would strand the line against crossed-out edges or a grid corner, the edge is off. This "assume and walk one step" test is not guessing — you are proving a contradiction on a single edge, and the answer is immediate.

The loop must be one loop

Late in a puzzle, the strongest remaining constraint has nothing to do with the numbers. If joining two loose ends would close a small loop while segments still sit outside it, that join is illegal — the solution must be a single loop containing everything you have drawn. This one rule resolves the final ambiguity on most boards, and it is the reason a Slitherlink never needs a guess.

The same idea works in reverse for tracing the boundary. Every clue cell is either inside or outside the loop, and neighbouring cells that are both inside or both outside have their shared edge off. Colouring cells inside/outside as you go turns a fiddly edge puzzle into a much more visual one, and many expert solvers work almost entirely in that colouring.

A reliable order of attack

1. Cross out every side of every 0.
2. Apply the corner rules for 1s and 3s on the border.
3. Find adjacent and diagonal 3 pairs and place their forced edges.
4. After every edge you draw, resolve both of its dots.
5. Sweep clues whose remaining free sides exactly match their remaining count.
6. Near the end, use the single-loop rule to reject any join that would close early.

Work in that order and the board opens in waves — a couple of forced edges create dot constraints, those constraints satisfy nearby clues, and those clues force more edges. If you ever feel the urge to guess, go back and check the dots you have not revisited since your last few segments. The forced move is almost always sitting there.