What Makes a Slitherlink Puzzle Hard?

It's Not Just Size

You might think a 20x20 puzzle is harder than a 10x10. Often true, but a 10x10 "Hard" can be more brain-melting than a 20x20 "Easy." What actually drives difficulty?

1. Clue Density

Paradoxically, fewer numbers often mean a harder puzzle. A grid full of numbers gives you constant local feedback. A sparse grid forces you to rely on long-range loop logic ("global connectivity") because you can't just check neighbors.

Compare these two grids — same size, very different difficulty:

  Easy (dense clues):          Hard (sparse clues):

  · ─ · ─ · ─ · ─ ·           · ─ · ─ · ─ · ─ ·
  │ 3   0   3   2 │           │       2       │
  · ─ · ─ · ─ · ─ ·           · ─ · ─ · ─ · ─ ·
  │ 2   3   1   3 │           │           1   │
  · ─ · ─ · ─ · ─ ·           · ─ · ─ · ─ · ─ ·
  │ 0   1   2   0 │           │   1           │
  · ─ · ─ · ─ · ─ ·           · ─ · ─ · ─ · ─ ·

  Many 0s and 3s → fast!      Few clues, all 1s/2s → hard!

2. The Role of 1s and 2s

0s and 3s are "easy" numbers—they are highly constrained.
1s and 2s are "hard" numbers—they have many valid states.
An "Easy" puzzle is packed with 0s and 3s. A "Hard" puzzle is dominated by 1s and 2s, often in the middle of the board with no borders nearby.

3. Clue Distribution

Clustered clues are easier. If numbers are touching, they interact and eliminate possibilities. Scattered clues (a number here, a number there) don't interact, forcing you to bridge the gap with empty cells, which is much harder logic.

4. Difficulty Levels Explained

  Easy                Medium              Hard
  ┌───┬───┬───┐      ┌───┬───┬───┐      ┌───┬───┬───┐
  │ 3 │ 0 │ 3 │      │ 2 │   │ 3 │      │   │   │ 2 │
  ├───┼───┼───┤      ├───┼───┼───┤      ├───┼───┼───┤
  │ 2 │ 3 │ 0 │      │   │ 1 │   │      │   │ 1 │   │
  ├───┼───┼───┤      ├───┼───┼───┤      ├───┼───┼───┤
  │ 1 │ 2 │ 3 │      │ 3 │   │ 2 │      │   │   │   │
  └───┴───┴───┘      └───┴───┴───┘      └───┴───┴───┘
  Dense, many 3s/0s   Mixed clues         Sparse, mostly 1s/2s
  1-step deduction    Some look-ahead     Global loop logic

• Easy: High density of clues. Many 0s and 3s. Lots of edge clues. Logic is mostly local (1-step deduction).
• Medium: Balanced mix. Requires some "Diagonal 3" or "Corner 2" knowledge. Requires tracking the loop for short distances.
• Hard: Sparse clues. Mostly 1s and 2s. Requires "Jordan Curve" logic (inside/outside) and contradiction testing ("If I go here, I eventually crash 10 steps later").

Building Up

If you find Hard puzzles frustrating, it's likely because you haven't mastered the patterns of 1s and 2s yet. Go back to Medium and focus specifically on how those numbers behave. Once you can "see" the flow through a 2, the Hard puzzles become approachable challenges rather than impossible walls.