How to play Slitherlink
A grid of dots with numbers between them. Join neighbouring dots with short lines to make one closed loop: no crossings, no branches, no loose ends. Each number says how many of the four sides of its square the loop runs along.
A blank square can have any number of sides on the loop. The 5 × 5 is a warm-up; the 10 × 10 runs to about ninety lines.
Rules
- Lines join dots side by side or one above the other, never diagonally. Every dot the loop touches has exactly two lines; every other dot has none.
- A 0 has no lines around it and a 3 has three. A 2 can have opposite sides or two sides meeting at a corner.
- There is only one loop. Two separate loops, even if each fits its numbers, are not a solution.
- Mark an edge with a cross when you know the loop doesn’t use it. Crosses are only notes; they don’t have to be complete to solve.
- A number met exactly fades. A number with too many lines, or too few open sides left, turns red, as does a dot where the line branches or dead-ends, and a closed loop that leaves other lines outside it.
- Each size has its own saved puzzle and its own best time. The clock stops while the tab is hidden.
Controls
- Click / tap an edge
- Cycle line → cross → empty
- Drag
- Draw a run of lines from dot to dot (start on a line to erase a run)
- Right-click
- Toggle a cross (drag to cross out several)
- Arrows / WASD
- Move the cursor over dots and edges
- Shift + arrow
- From a dot, draw a line that way and follow it
- Space / Enter
- Cycle the edge under the cursor
- L / X
- Toggle a line / a cross
- Backspace
- Clear the edge
- Z / Ctrl+Z
- Undo
- P
- Pause
Tips
- Start with the 0s: cross out all four sides. Then a 3 next to a 0 is easy, and a 3 in a corner of the grid always takes the two outer sides.
- A dot with no lines and only one open edge can’t be on the loop, so cross that edge out. A dot with one line and one open edge must continue along it.
- Two 3s side by side share their middle edge and both outer edges across from it: draw all three parallel lines.
Slitherlink strategy
Corners as gates
Look at each corner of a number as a gate: the loop either passes through that dot or it doesn’t. If both edges leading away from a 1’s corner are crossed, the line can’t turn through there, so the 1’s two sides at that corner are crossed too. The same picture next to a 3 forces both of its sides at that corner to be lines. The corners of the grid are gates with nothing outside, which is why a 1 there loses both outer sides and a 3 takes them.
Pairs of 3s
Two 3s side by side take their shared edge and the two edges parallel to it on the far sides, and the short edges that continue the shared one above and below are crossed. Two 3s touching at a corner take the two outer sides at each far corner, since the loop has to wrap around both of them.
No early loops
When the two ends of one line are a single edge apart, that edge stays empty unless closing it would finish the puzzle: one loop has to take in every line. Watch for it near the end, when two long strands creep towards each other and a shortcut would seal them off.
Inside and outside
Every square is either inside the loop or outside it, and crossing a line switches sides. Squares beyond the rim are outside. A 0 sits on the same side as its four neighbours; a 3 differs from three of them. When counting stalls, shading what you know to be inside in your head often shows which edges have to be lines.
One step of what if
Every puzzle here is settled by counting plus one-step what-if checks, so when you are stuck there is always an edge where one choice runs into a contradiction. Draw it, follow the forced moves until a number or a dot breaks, then undo and mark the other way. The clock keeps running, so pick an edge in a crowded corner, where the forced moves come quickly.
About Slitherlink
Slitherlink is a Nikoli puzzle. It first appeared in Puzzle Communication Nikoli issue 26 in June 1989, where the editor combined two puzzles sent in by readers. At first every square held a number and the lines didn’t have to make a loop.
Here a random loop is grown on the grid, every square is numbered, and numbers are taken away one by one while a solver can still settle every edge by counting plus one-step “what if” checks. So each puzzle has exactly one loop, and you never need more than one step of trial to find it.
Questions
How do you solve Slitherlink?
Use the numbers to decide which edges are lines and which are not, and keep the dots honest: each has two lines or none. Starting from the 0s and 3s usually opens the first corner of the loop.
Does every Slitherlink have one solution?
Yes. Each puzzle is checked by a solver that only makes forced moves and one-step what-if checks, and it settles every edge, so there is exactly one loop.
Can the loop touch itself?
No. It is one closed line that never crosses, branches or touches itself at a dot, since every dot on it has exactly two lines.
What do blank squares mean?
Nothing is known about them: the loop may run along none, some or all but one of their sides. Only numbered squares give a count.
