Slitherlink Rules
Everything you need to know, from the basic rules to the deduction patterns that make this puzzle work.
The rules
A slitherlink grid is a lattice of dots. The segments between adjacent dots are edges, and the rectangular spaces between four dots are cells. Some cells contain a number from 0 to 3.
Rule 1 — Number clues: each number tells you how many of that cell's four edges (top, right, bottom, left) are part of the loop. A 0 means none of its edges have lines. A 1 means exactly one. A 2 means two. A 3 means three. Cells without a number have no constraint on their edge count.
Rule 2 — Single closed loop: all line segments must connect into exactly one closed loop. The loop cannot branch (no vertex with 3+ lines), cannot have dead ends (no vertex with exactly 1 line), and cannot split into separate disconnected loops.
That's the entire ruleset. Two rules. No row or column constraints, no regions, no arithmetic. The difficulty comes from the interaction between local number clues and the global single-loop requirement.
Number clues in detail
0 — no edges at all
A cell with a 0 contributes nothing to the loop. All four of its edges are excluded. This is the most immediately useful clue: mark all four edges with × marks right away. The exclusions propagate to neighbouring cells, often resolving their clues too.
1 — exactly one edge
One of the cell's four edges is a line, and three are excluded. You rarely know which edge is the line from the 1 alone — it usually requires information from adjacent clues or vertex constraints. A 1 in a corner of the grid is special: two of its edges are on the boundary, and vertex constraints at the corner often force two of the remaining edges to be excluded, leaving the line determined.
2 — exactly two edges
Two edges are lines, two are excluded. The loop passes through the cell — it enters on one edge and exits on another. The two line edges can be adjacent (the loop turns at the cell) or opposite (the loop passes straight through). Context determines which configuration is correct.
3 — three out of four edges
Only one edge is excluded. This is the second most immediately useful clue after 0. A 3 in any corner of the grid forces two specific edges (the boundary edges). If you can determine which single edge is excluded, the other three are all lines. Adjacent clues, vertex constraints, or loop-closure reasoning usually make this determination straightforward.
Solving techniques
1. Fill in 0s and corner 3s immediately
A 0 means all four edges excluded. A 3 in a grid corner forces two lines on the boundary edges. These are free placements that require no deduction. Fill them first and their effects ripple outward.
2. Edge counting
For any numbered cell, count how many edges are already lines and how many are excluded. If the line count equals the clue, all remaining edges are excluded. If the excluded count equals (4 minus the clue), all remaining edges are lines. This is the technique you will use most often.
3. Vertex constraints
Every vertex (dot) has either 0 or 2 line edges. If a vertex has 2 lines, exclude the rest. If a vertex has 1 line and only one more possible edge, that edge must be a line (the loop can't dead-end). Apply this after every edge placement.
4. Adjacent 3-3 pattern
Two 3s sharing an edge means that shared edge is always a line. The four outer edges perpendicular to the shared side are also forced. This gives you five edges from two clues.
5. Adjacent 3-0 pattern
A 3 next to a 0 means their shared edge is excluded (because the 0 allows no edges). The three remaining edges of the 3 must all be lines. You get three edges plus four exclusions from this two-cell pattern.
6. Loop closure prevention
The single-loop rule says all lines must form one connected loop. If drawing a line between two vertices that are already connected by an existing path would close a sub-loop that doesn't include all placed lines, that edge must be excluded. This constraint gets more useful as the grid fills up.
7. Region parity
On harder puzzles, you can reason about regions. The loop divides the grid into inside and outside. If two cells must be on the same side (both inside or both outside), the edge between them is excluded. If they must be on opposite sides, the edge between them is a line. This technique appears mainly on expert and Einstein grids.
Tips
- Mark exclusions (× marks) as aggressively as you draw lines. Knowing what's outside the loop is half the puzzle.
- After every edge placement, re-check the two vertices at its endpoints for new constraints.
- Scan for 0s and 3s first on every puzzle — they are the fastest starting points.
- Track connectivity. Two endpoints of the partial loop that meet should only close when the loop is complete.
- On grids 10×10 and larger, work in clusters. Exhaust local deductions before looking for long-range chains.
Common mistakes
Forgetting the loop constraint. New players often satisfy all number clues but end up with branches or multiple separate loops. The lines must form one single closed path. Check vertices regularly — any vertex with 1 or 3+ lines means something went wrong.
Ignoring blank cells. Cells without numbers can have 0, 1, 2, 3, or 4 edges as lines. New players sometimes treat them as 0s and exclude all their edges. Blank cells are unconstrained by the number rule but still subject to vertex and loop constraints.
Not marking exclusions. Without × marks, you lose track of which edges you've ruled out. This leads to re-checking the same cells repeatedly and missing forced moves. Mark exclusions immediately as you determine them.
Closing the loop too early. If you connect the two endpoints of your partial loop before all line edges are placed, you get a small closed loop and a bunch of orphaned line segments. Always check: does closing this edge account for all placed lines?
Frequently asked questions
What are the rules of Slitherlink?
Draw line segments along grid edges to form a single closed loop. Each numbered cell (0–3) tells you how many of its four edges are part of the loop. The loop cannot branch, cannot have dead ends, and must be fully connected.
How do you solve a Slitherlink puzzle?
Start with 0s (exclude all edges) and corner 3s (two forced lines). Use edge counting: match placed lines and exclusions against the number clue to determine remaining edges. Check vertex constraints (0 or 2 lines per vertex). On harder puzzles, track loop connectivity to prevent premature closure and use region analysis.
What is Loop the Loop puzzle?
Loop the Loop is another name for Slitherlink, used in some British puzzle books and magazines. The puzzle is also published as Fences or simply Loop Puzzle. Same rules in every case.
Is Slitherlink harder than Sudoku?
Different skills, different challenges. Sudoku is pure number placement with row/column/box constraints. Slitherlink adds a topological constraint (the single loop) that many solvers find initially unfamiliar. At equal difficulty levels, most experienced puzzlers rate them as comparable — though Slitherlink's loop rule makes mistakes harder to spot.
Can you solve Slitherlink without guessing?
Yes. Well-made Slitherlink puzzles have a unique solution reachable through logic. Our Einstein puzzles are certified solvable without any guessing — every edge is determinable through constraint propagation and deduction alone.
Related puzzle rules
- Hashi rules — Connect islands with bridges to form a network
- Futoshiki rules — Fill a grid with inequality constraints
- Nonogram rules — Deduce filled cells from row and column clues