Slitherlink techniques

Zero Clue

A 0 means no edge of this cell can be part of the loop — mark all four sides with an X.

Full Clue

A 4 means every edge of this cell is part of the loop — draw all four sides as lines.

Clue Satisfied

Once a clue's line count is already met, every other side of that cell is ruled out; once a clue needs every remaining side, all of them are forced in.

Corner Clue

A grid corner's two outer edges always match — both lines or both blank, since the corner dot only touches those two edges. A clue of 1 or less rules both out; a clue of 3 or more forces both in.

Every dot needs exactly zero or two lines touching it, never one. A dot with two lines already has its rest ruled out; a dot with only one edge left has that edge forced by how many lines it already has.

Loop Avoidance

Drawing this edge would close a loop right now. If closing it here can't be the whole solution, it's ruled out — but if closing it here does satisfy everything, it's the final edge, so it's forced in.

Adjacent Clue Pair

Two clued cells sharing an edge only have a few ways to satisfy both clues at once — any side none of those ways use is forced, one way or the other.

Adjacent 3s

Two 3s side by side: the outer edge of each one — the side facing away from its partner — is always a line.

0 Beside a 3

A 0 next to a 3 settles the 3 outright: the shared edge is blank, so the 3's other three sides are all lines.

Diagonal Clue Pair

Two clued cells touching only at a corner still constrain each other through that shared dot — any side no valid combination uses is forced.

Diagonal 3s

Two 3s touching only at a corner: the two outer sides of each — the ones away from the shared dot — are all lines.

3 Diagonally Opposite a 0

A 3 catty-corner from a 0: the 3's two sides that reach the shared dot are both lines.

Three-in-a-Row

Three clued cells in a row or column, checked together, rule out combinations a single pair can't catch alone — including the classic 1-2-1 and 2-2-2 patterns.

Three 3s in a Row

3-3-3 side by side: all four vertical edges crossing the run are lines.

Quad Window

A 2x2 square of cells, checked as one block: every clue in it plus the dot they all share (and any board-edge dots along it) usually leave only a few possible ways to draw the lines. Any side those ways all agree on is forced.

Crossing Parity

The loop is closed, so any straight line drawn across the whole board crosses it an even number of times. When every crossing edge in a row or column is decided but one, that last edge is forced — whatever makes the count even.

Sector Chain

A sector is the pair of a cell's sides meeting at one of its corners, and the loop uses 0, 1, or 2 of them. A 2 passes the same count to its opposite corner, and every dot passes it on diagonally, so the fact travels along a whole chain of sectors. A chain seeded at a border or a 3 forces edges far from where it started.

Sector Parity

Each cell has four sectors, one per corner, and the number of them holding exactly one line is always even. Once three of a cell's four sectors are pinned to "exactly one" or "never exactly one", the fourth is settled — even when its own two sides are both still blank.

Dead End

A line can never just stop — every dot touches zero or two line segments. Draw a candidate edge and follow where the line is forced to go: if it gets driven into a dot whose other edges are all crossed off, it dies in a dead end, so the candidate edge is ruled out.

Six-Cell Window

The same block check widened to a 2x3 or 3x2 rectangle — six cells at once. Slower to work through, but it catches clue clusters that bend around a corner, which no straight-line or square window can see.

Region Coloring

Shading every cell as inside or outside the loop (with the space beyond the grid always outside): a line always separates two different shades, a blank always keeps the same shade. Chaining that logic across the board pins down edges too far apart for any single clue to reach alone.

Connectivity

The finished loop is a single connected shape, so every line already drawn has to end up joined to every other one. An edge whose removal would cut one group of lines off from another is forced in; an edge marooned in a pocket the drawn lines can never reach is ruled out.

Contradiction

When nothing else advances the puzzle, try one edge's two possible states and follow the consequences a few steps ahead. If one choice breaks a clue or a dot's rule, drives a line into a dead end, or finishes the board as anything but one single loop, the other choice is forced.

Highlander

Uses the fact that the puzzle has exactly ONE solution: any move that would leave two different valid answers must be wrong. Powerful, but it's reasoning about the puzzle rather than about the loop.

Trial and Error

Guessing, and the only place the puzzle asks for it. Pick a side, commit to it, and keep solving as far as it goes — if it eventually dead-ends, the other side was right all along. Only Extreme puzzles are ever built to need this.