Slitherlink (Fences) Puzzle

Slitherlink is a loop puzzle, and it is also called Fences. You join the dots of a grid into one closed loop, using the numbers as a guide to how many sides of each cell the loop runs along. Every puzzle here has exactly one solution that you can reach by logic, with no guessing.

Rules

The board is a grid of dots. A line can join two dots that sit next to each other across or down, never diagonally.

Draw lines to make a single closed loop. The loop never crosses or touches itself and never branches, so every dot on it has exactly two lines and every other dot has none.

A number from 0 to 3 in a cell says how many of that cell’s four sides are part of the loop. A cell with no number can have any count.

The puzzle is solved when the lines form one loop and every number has exactly that many lines around it. Sides you leave empty don’t need a cross.

Controls

Tap between two dots to draw a line there, and tap the line again to clear it. Each side of a cell owns the area nearest to it, so you don’t have to hit the thin line exactly. To draw several sides at once, press on a dot and drag through the next dots; dragging back over the last step takes it off again before you let go.

Switch the tool under the board to Cross to mark sides that can’t be part of the loop. With a mouse, a right-click or a right-drag always draws crosses. Starting a drag on a side that already has the tool’s mark clears instead, so the same gesture erases a run.

Auto-× is on to begin with. As soon as a number has all its lines, its other sides get crosses in the same undo step. It never draws a line for you, and you can turn it off with the button under the board.

A number with too many lines, a number that can no longer reach its count because too many of its sides are crossed, a dot with three or more lines, and a small closed loop while other lines are still elsewhere all turn red at once. Press Hint for one side the rules already force, with a sentence saying why. Press Check when you want the board scored against the rules. Undo and Redo step through your moves, and Reset clears the board.

On a keyboard, the arrow keys move a cell cursor, Shift with an arrow toggles that side of the cell, and X switches between Line and Cross.

Techniques

Easy grids need counting only:

• Zeros: a 0 has no line on any side, so cross all four.
• Corners: a 3 in a corner of the grid uses both border sides, and a 1 in a corner leaves both border sides empty.
• Full numbers: once a number has all its lines, its other sides are empty. If its open sides are exactly the lines it still needs, they are all lines.
• Dots: a dot with two lines is full, so its other sides are empty. A dot with one line and one open side must continue through it, and a dot with no line and one open side is a dead end, so that side is empty.
• No early loops: a side that would close a small loop while other lines are still apart can’t be a line.

Medium grids also need pairs of sides at a corner. Look at the two sides that meet at one dot of a cell. Sometimes the numbers force exactly one of them to be a line, or rule out both being lines, even before you know which one. That fact travels to the next cell along the same dot.

Hard grids need a wider view:

• Parity: the loop is closed, so it crosses any straight cut across a row or a column an even number of times. If only one side along the cut is still open, the count decides it.
• Inside and outside: every cell is either inside the loop or outside it. Two neighbouring cells on different sides have a line between them, and two on the same side don’t.

Beginner tips

Start with the 0s and with any 3 next to a 0 or in a corner. Cross every side of each 0 first; that alone usually fixes several lines nearby.

Follow loose ends. A line that stops at a dot has to carry on somewhere, and often only one direction is still open.

Keep Auto-× on while you learn. The crosses it adds narrow the choices around each number, so the next step is easier to see. If you are new to Slitherlink, start with a 5×5 and move up to 7×7 easy once the corner patterns feel natural.