, abbreviated or, is a binary-determination logic puzzle published by Nikoli. A book consisting entirely of puzzles has been published by Nikoli.
is played on a rectangular grid. Some of these cells have numbers in them. Each cell may be either black or white. The object is to determine what type each cell is.
The following rules determine which cells are which:
A number of methods of solving puzzles exist.
Any cell with a number in it must be white; this is very important. For example, a 2 cell with another numbered cell next to it would be visible from the 2 cell, and no other cells can be visible from the 2 cell. Therefore, all neighbouring cells to the 2 cell must be black. The cell beyond the other numbered cell must also be black. This is one method of starting some puzzles.
Another method of beginning some puzzles starts from a 2 cell and another numbered cell or white cell in the same row or column, with just one space between them. The cell in the middle must be black, as if it were white, the 2 cell would be able to see at least 3 cells.
If the number inside a cell is equal to the maximum number of cells it could possibly see, then all those cells must be white in order for that maximum to be possible. For example, in a 7×7 puzzle, the maximum number that can be had in any cell is 13 (the cell itself, plus six others in the row, plus six other in the column). If a 13 appears in a cell of a 7×7 puzzle, all cells in the same row or column as the 13 must be white. This is often represented by placing dots in those cells.
Deciding if a puzzle is solvable is NP-complete.[1]
is an original puzzle of Nikoli; it first appeared in Puzzle Communication Nikoli #34 (June 1991). The English language Nikoli website uses Engrish to translate the name as "Where is Black Cells".