Shade the sea around the numbers so each clue becomes an island of exactly its size, with the water flowing as one connected piece.
Every numbered cell is part of an island made of that many cells. Shade the remaining cells as sea. Each island must be exactly its number's size and contain exactly one number, islands may never touch edge to edge, all the sea must connect into a single region, and the sea can never form a solid 2x2 block.
Published in Japan as Nurikabe and named for a yōkai, a wall-spirit that blocks travellers on a night road, this puzzle was created by a designer whose pen name れーにん is the Japanese pronunciation of "Lenin".
It appeared in the 33rd issue of Puzzle Communication Nikoli in March 1991 and caused enough of a sensation that it has run in every issue from the 38th onward. By 2005 Nikoli had published seven books consisting of nothing else.
The solving idea is one of inversion. You are given the sizes of the islands but not their shapes, and the real work happens in the sea between them — the wall must be continuous, may never form a 2×2 block, and it is usually the sea that tells you where an island cannot reach.
Islands is a logic puzzle in the shade-the-grid family, where number clues, connectivity, and the no-2x2 rule combine into pure deduction. This is an original, free browser version with daily and practice puzzles, no download or sign-up required.