How to solve Nurikabe: building islands in a single sea

The rules

• Each number belongs to a white island of exactly that many cells.
• Every island holds exactly one number; islands never touch side by side.
• All shaded cells form one connected sea.
• The sea never contains a 2×2 block of shaded cells.

First steps

• A 1 is a finished island: shade all four neighbours.
• A cell that touches two numbers side by side (for example the gap in 3 _ 2) can't join either island without merging them, so it's sea.
• A cell that no island can reach (too far from every number for its size) is sea.

Growing and closing islands

When an island has only one way to grow, extend it. A 2 in a corner with one neighbour already sea has one cell left to take. Once an island reaches its size, wall it off: every cell touching it becomes sea.

No 2×2 pools

If three cells of a 2×2 square are sea, the fourth must be island, and some number has to reach it. That's often what decides which way an island grows: the island that can reach the gap must use one of its cells there.

Keep the sea connected

A patch of sea that's boxed in by islands must escape somewhere. If it has only one exit, the cell at that exit is sea. Near the end, check every sea region: they must all join into one.

A solving routine

1. Shade around every 1, and shade cells that touch two numbers.
2. Shade cells too far from every number to belong to an island.
3. Extend islands that have only one way to grow; wall off finished ones.
4. Break up every 2×2 pool by finding the island that must reach it.
5. Make sure the sea stays connected, and repeat.

Practise

On Puzzimo, tap a cell to dot it • as island (tap again to clear), double-tap to shade it ■ as sea, and drag to mark many cells at once. Shading a cell that belongs to an island counts as a mistake: it's shown and corrected, and the third ends the round. Grids come in 5×5, 6×6 and 7×7, with a 6×6 daily challenge.

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