Slitherlink is a logic puzzle where you draw a single closed loop on a grid using number clues. Each number tells you how many of its four surrounding edges are part of the loop. No number? That cell could have any count.
Corners are where you should always start solving — they have fewer edges (only 2 outer edges touching the grid boundary), which means fewer possibilities and faster deductions.
The Rules, Briefly
- Draw lines on grid edges to form one continuous closed loop
- Each number = count of lines around that cell
- The loop cannot branch or cross itself
- Every vertex (dot) has either 0 or exactly 2 lines passing through it
Corner 0: Instant Elimination
A 0 in the corner means zero lines around it. Since a corner cell has only 2 outer edges, both are eliminated immediately — plus the 2 inner edges.
· · ·
× 0 ×
· × · × ·
Why it works: 0 means no lines at all. Mark all 4 edges with × and move on. This is the single fastest deduction in the game.
Pro tip: After marking a corner 0, check the adjacent cells. If there's a 3 next to a 0, you just eliminated one of the 3's edges — forcing the remaining 3 edges to all have lines.
Corner 3: Two Guaranteed Lines
A 3 in the corner needs 3 out of 4 edges to have lines. But the corner vertex only connects to 2 outer edges. If either outer edge had no line, the vertex would need the line to come from somewhere — but there's nowhere else to go without violating the loop rule.
·───· ·
│ 3
· · ·
Both outer edges must have lines. That gives you 2 out of 3 lines immediately. The third line is one of the 2 inner edges — you'll determine which one from neighboring clues.
Why it works: Consider the corner vertex (top-left). The loop requires 0 or 2 lines at each vertex. The outer edges are the only ones connecting to this vertex. If one were missing, you'd have exactly 1 line at the vertex — a dead end, which is illegal.
Corner 1: Both Outer Edges Are Empty
This one surprises beginners. A 1 in the corner means neither outer edge can have a line.
· × · ·
× 1
· · ·
Why it works: Suppose one outer edge has a line. The corner vertex now has exactly 1 line. To satisfy the vertex rule (0 or 2 lines), the other outer edge must also have a line — but then we'd have 2 lines, making this cell at least a 2, not a 1. Contradiction.
So both outer edges must be ×, and the single line for this 1 comes from one of the 2 inner edges.
Corner 2: The Paired Pattern
A 2 in the corner has an elegant constraint: the two outer edges are always the same — either both have lines, or both are empty.
Case A — both outer edges have lines (2 of 2 accounted for, inner edges empty):
·───· ·
│ 2
· · ·
Case B — both outer edges empty (both lines come from inner edges):
· · ·
2
· × ·───·
Why it works: If only one outer edge had a line, the corner vertex would have exactly 1 line — a dead end. So they must match: both on or both off. You need more information from neighboring cells to determine which case applies.
Combining Corner Patterns with Neighbors
Corner 3 + Adjacent 3 (The S/Z Shape)
When a corner 3 sits next to another 3, you get one of the most powerful patterns in Slitherlink — 5 edges determined at once:
·───· ·───·
│ 3 │ 3 │
· ·───· ·
The shared edge between the two 3s always has a line. Combined with the corner 3's two outer lines, and the second 3 needing its own 3 lines, you get an S-shaped (or Z-shaped) pattern.
Mirror version:
· ·───· ·
│ 3 │ 3 │
·───· ·───·
Corner 3 + Adjacent 0
When a 0 sits next to a corner 3, the 0 eliminates their shared edge. Since the corner 3 already has 2 outer lines, the third line must go to the remaining inner edge:
·───· · ·
│ 3 × 0 ×
·───· × · × ·
All 3 of the corner 3's lines are now fully determined.
The Vertex Rule: Why These Patterns Work
Every pattern above derives from one principle: each vertex has 0 or 2 lines.
This is because the loop is continuous — if a line enters a vertex, it must also leave. No dead ends allowed. This constraint, combined with corner geometry (only 2 outer edges meet at the corner vertex), makes corners the most constrained — and therefore most solvable — cells on the board.
Practice Strategy
- Scan all 4 corners first — process 0s, 3s, and 1s immediately
- Check neighbors of corner cells — propagate constraints outward
- Look for edge cells next — they have 3 edges (1 outer), similar constraints
- Work inward — interior cells have 4 edges and need more context
Start with easy 5×5 puzzles where corners dominate the grid. As you scale to 10×10 and 15×15, corner patterns still fire first — but you'll need intermediate and advanced techniques for the interior.
Try these patterns on real puzzles: slitherlinks.com — 3000+ free puzzles across 5 grid sizes and 10 difficulty levels. Start with 5×5 Level 1 to practice corner patterns in isolation.
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