Hitori

From Wikipedia, the free encyclopedia

Example of an incomplete Hitori puzzle (see bottom of page for solution)

Hitori (ひとりにしてくれ Hitori ni shite kure; literally "let me alone") is a type of logic puzzle published by Nikoli.

1 Rules
2 Solving techniques
3 History
4 References
5 See also
6 External links
- 6.1 Variants

[edit] Rules

Hitori is played on a grid of squares. At the beginning, each cell contains a number. The goal is to paint out some cells so that there are no duplicate numbers in any row or column, similar to the solved state of a Sudoku puzzle (except with black squares added to the grid).

Orthogonal connections are important as well; painted-out (black) cells cannot be connected orthogonally, and the other cells must be connected orthogonally in a single group. (i.e. no two black squares can be adjacent to each other, and all un-painted squares must be connected, horizontally or vertically, to create a single shape.)

[edit] Solving techniques

An easy starting place is a sequence of three identical numbers; the centre number must be white as if it was black it would have to be next to another black square; both ends must be painted out to satisfy the rules.
When it is confirmed that a cell must be black, one can see all 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.
When two identical numbers are adjacent and the row or column also includes another identical number then the single number must be black - leaving it white would result in the two adjacent numbers being black, which is not permitted.
Any cells which if painted would segregate a group of circled white numbers from the rest of the puzzle must be white and can therefore be circled.
Any number which is on the same row or column as an identical circled white number must be black.
Any number that is adjacent to two identical numbers on opposite sides of the cell must be white as one of the adjacent numbers has to be black and cannot be adjacent to another black cell.
When four identical numbers are in a two by two square on the grid there must be two black cells along a diagonal. There are two possible combinations, and it is sometimes possible to decide which is correct by considering if one or the other variations will cut white squares off from the remainder of the grid.