Nurikabe: walls and reach
A finished island is walled in by sea. A cell that touches two islands is sea. And a cell no island can reach is sea too.
How it works
Every cell in Nurikabe is either sea or part of a numbered island. These three moves prove a cell is sea, and they work from the very first look.
Walls: an island that has reached its size can’t grow, so every open cell beside it is sea. A 1 is finished from the start.
Between: a cell that touches two different numbered islands would join them, and an island holds one number. So it is sea.
Reach: an island with number v and k cells can still add v − k cells. Any cell farther than that from every island is out of reach, so it is sea.
Counting reach
Count steps out from the island’s cells, not from the number. An island of 2 cells with a 5 can add 3 more, so it reaches 3 steps from any of its cells.
A path can’t pass beside another numbered island, because that would join the two. And it can’t cross sea. So walls you have already drawn cut reach down.
Worth memorizing
Every cell beside a 1 is sea.
The same goes for any finished island.
A cell touching two numbers’ islands is sea.
Out of reach means sea.
Reach is the number minus the cells the island already has.
Practice
0 of 4 rightWhat is the ringed cell?
Using only walls and cells between numbers, what is the ringed cell?
How many more cells can the 5 add?
What is the ringed cell?