5 Essential Slitherlink Solving Techniques

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Slitherlink is a game of patterns. While you can solve easy puzzles with intuition, harder grids require a toolkit of proven techniques. Here are the 5 essential patterns every solver needs to know.

Technique 1: Corner Clues

Corners are the easiest place to start because the grid boundaries limit the possibilities.

Example: Corner 3
A 3 in a corner is the most powerful. It forces lines on both outer edges immediately.

·───·   ·
│ 3      
·   ·   ·

• 0 in a Corner: Both edges touching the corner point must be empty (marked with X). In fact, for a 0 anywhere, all 4 sides are X.
• 1 in a Corner: The two outer edges (forming the corner of the grid) cannot both be lines, because that would leave a loose end at the corner point. But this clue is generally weak on its own.
• 2 in a Corner: If you have a 2 in a corner, the two outer edges must either be BOTH lines or BOTH empty.
• 3 in a Corner: This is a golden clue! A 3 in a corner MUST have lines on the two outer edges. If it didn't, it would be impossible to satisfy the "3" count without creating a branch or loose end.

Technique 2: Adjacent 3s

When two "3" clues are next to each other (sharing an edge), they force a specific pattern.

Imagine two 3s side-by-side: 3-3. The shared edge between them MUST be a line. Furthermore, the two outer edges parallel to the shared edge must also be lines. The lines effectively wrap around the pair. You can instantly fill in three lines just by seeing a 3-3 pair.

·───·   ·───·
│ 3 │ 3 │
·   ·───·   ·

Technique 3: Diagonal 3s

When two "3" clues touch diagonally (sharing a vertex), they also restrict the board heavily. The two outer edges that meet at the shared vertex MUST be lines. This is a very common pattern in medium and hard puzzles. Recognizing this instantly gives you two free lines.

Technique 4: The 0 Clue Elimination

The number 0 is powerful because it clears space. If you see a 0, mark X's on all four sides immediately.

·   ·   ·
  × 0 ×  
· × · × ·

But the power of 0 extends to its neighbors. If a "3" is adjacent to a "0", that "3" effectively becomes a corner case (or worse/better). Since the side shared with the 0 is blocked, the other 3 sides of the "3" MUST be lines. A 3 next to a 0 is a solved cell!

·   ·───·   ·   ·
    │ 3 × 0 ×    
·   ·───· × · × ·

Technique 5: Loop Closure Logic (The Jordan Curve Theorem)

This is a more advanced concept but vital for hard puzzles. Remember, there is only ONE loop. It cannot intersect itself.

If you have a path that enters a region and you have two possible exits, think about what happens if you close the loop too early. Small, closed loops that are separate from the main loop are forbidden. If placing a line would create a tiny, isolated box, you know that line is impossible (mark it X).

Similarly, "coloring" logic can be used. The loop divides the grid into "inside" and "outside." If you know one square is inside, you can deduce the status of its neighbors across lines (inside -> outside) or across empty boundaries (inside -> inside).

Vertex Logic
Always remember the vertex rule: if a point has 2 lines, no other lines can connect to it.

·───·
│    
· × ·

Practice Makes Perfect

Don't try to memorize these all at once. Start playing, and when you get stuck, come back to this list. Look for corners, look for 3s, and look for 0s. These three clues are the bread and butter of Slitherlink solving.