Nurikabe

Nurikabe is played on a rectangular field divided into square cells of the same size. Initially, all cells are white (not filled in), some of them contain numbers.

The player’s task is to color the cells in such a way as to divide the field into “islands” consisting only of white squares. The islands should be separated from each other by black squares, forming a common network (a conventional “river”). Moreover, each island must consist of such a number of squares that corresponds to the number placed on it.

Game rules

In Nurikabe, two cells are considered connected if they are adjacent to each other horizontally or vertically (but not diagonally). Thus, an island can be considered a single white cell, or several cells arranged in a row or column. It is also possible to construct more complex figures. The main thing is that 3 basic rules are followed:

• Each numbered cell is a part of the island, and its number corresponds to the number of cells that make up it.
• One island can contain only one numbered cell.
• A conditional river of black cells should form a common network, and not contain areas of size 2x2 or more.

From a mathematical point of view, Nurikabe's solution is NP-complete, and it is extremely unlikely (almost impossible) that a solution will be found for a puzzle with numbers randomly placed on the field. In the 90s, this greatly complicated the work of the compilers of such puzzles, who had to use all their skill and skill to create new editions. Today, this task has been extremely simplified through the use of computer technology and artificial intelligence.

Since the moves in Nurikabe are variable, many players use symbols on the playing field. For example, dots are used to mark cells that are likely to become part of the island.

How to solve the puzzle

Nurikabe's blind guessing tactics are extremely ineffective. You can win the game only with the help of logic and deduction. British writer and mathematician Alex Bellos noted in one of his books that in Nurikabe one has to constantly switch attention from islands to rivers. The player really needs to take turns going through the possible options for white and black cells, without forgetting about either one or the other.

This is a fairly exciting process that requires attention and concentration, but often causes difficulties for novice players. Especially for them, there are useful tips for playing Nurikabe, which look like this:

• The party should always start with cells numbered one. In 100% of cases, this is a single island, which can be immediately surrounded by black squares on four sides.
• Once the island becomes complete (that is, it includes the required number of white cells), all squares that have common sides with it can be painted black.
• When 3 or more black cells are folded into an L shape, the cells at the bend (diagonally from the top of the L) should remain white.
• All black cells at the end of the game must be connected to a common network. If at the final stage of the game there remains a separate black area with the only possible way to connect to the rest of the river, this opportunity must be used.
• All remaining white cells at the end of the game must be part of the islands. If there are empty white cells on the field with only one way to connect to the nearest islands, this opportunity must also be used.

Like most other puzzles from Nikoli, Nurikabe involves searching through possible moves and eliminating obviously losing ones. You need to paint over a cell only if you are absolutely sure that it is not part of the island. And for intermediate (not final) moves, you can use special marks on the field, for example, dots.