Hitori



Hitori (Japanese for: Alone or one person) (ひとりにしてくれ Hitori ni shite kure; literally "leave me alone") is a type of logic puzzle published by Nikoli.

Rules
Hitori is played with a grid of squares or cells, and each cell contains a number. The objective is to eliminate numbers by filling in the squares such that remaining cells do not contain numbers that appear more than once in either a given row or column.

Filled-in cells cannot be horizontally or vertically adjacent, although they can be diagonally adjacent. The remaining un-filled cells must form a single component connected horizontally and vertically.

Solving techniques

 * When it is confirmed that a cell must be black, one can see all orthogonally adjacent cells must not be black. Some players find it useful to circle any numbers which must be white as it makes the puzzle easier to read as you progress.
 * If a number has been circled to show that it must be white, any cells containing the same number in that row and column must also be black.
 * If a cell would separate a white area of the grid if it were painted black, the cell must be white.
 * In a sequence of three identical, adjacent numbers; the centre number must be white. If one of the end numbers were white this would result in two adjacent filled in cells which is not allowed.
 * In a sequence of two identical, adjacent numbers; if the same row or column contains another cell of the same number the number standing on its own must be black. If it were white this would result in two adjacent filled in cells which is not allowed.
 * Any number that has two identical numbers on opposite sides of itself must be white, because one of the two identical numbers must be black, and it cannot be adjacent to another black cell.
 * When four identical numbers are in a two by two square on the grid, two of them must be black along a diagonal. There are only two possible combinations, and it is sometimes possible to decide which is correct by determining if one variation will cut white squares off from the remainder of the grid.
 * When four identical numbers form a square in the corner of a grid, the corner square and the one diagonally opposite must be black. The alternative would leave the corner square isolated from the other white numbers.

History
Hitori is an original puzzle of Nikoli; it first appeared in Puzzle Communication Nikoli in issue #29 (March 1990).



In media

 * Episode 11 of xxxHolic: Kei is titled Hitori in reference to this.