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Nurikabe: Out of Reach

Each island can only grow as far as its number allows, and never right next to another island. A square that no island can reach is wall. It does more work than any other technique in Nurikabe.

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This is one of the Nurikabe techniques. Each page shows its technique on the same 8×8 from the game, Medium level 8.

The rule

  1. For each island, count how many squares it still needs.
  2. Mark every square it could reach in that many steps, going through empty squares and never touching another island.
  3. Any empty square no island can reach is wall.

In a real puzzle

On the 8×8, it’s first needed at step 7. Row 1, column 5 is too far from every number to be part of any island, so it’s wall.

Medium level 8, step 7 out-of-reach: wall row 1, column 5 (from row 1, column 5) 1 2 1 2 2 2 2 2 3 2 2 2 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Step 7: no island can reach row 1, column 5.

How often you’ll need it

On every one of the game’s 150 levels, more than any other technique: 10.6 times per Easy level on average, 15.8 on Medium and 22.6 on Hard. It’s 15 of the 42 steps on the 8×8 here.

Next steps

Questions

How far can an island reach?

As many steps as it still has squares to fill, without crossing wall or touching another island. A 3 with one square so far can reach two steps from it.