Hitori is played with a grid of squares or cells that contain numbers. The objective is to eliminate more than one of a number in every row and column. For instance, if you see two 5's in a row or column, one of the 5's must be taken out by shading in the square.
After shading a number, then circle the numbers that touch the shaded cell at right angles (but not diagonally). The circles will indicate that those cells cannot be shaded.
Shaded cells cannot be horizontally or vertically adjacent, although they can be diagonally adjacent. No circled cell can be completely isolated (cut off) from all other white cells.
1. 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 be shaded.
2. In a sequence of three identical, adjacent numbers (5-5-5), the center number MUST be shaded. The other two 5's would be circled. Why? Because if a number at the end of three identical numbers (like 5-5-5)is white, then then the other two would have to be shaded, and two shaded cells cannot be next to each other.
3. In a sequence of two identical adjacent number, if a row or column they are in has another identical number, the number that is by itself has to be shaded. If it were circled, then the two adjacent ones would have to be shaded. That is not allowed.
4. If a number has two identical numbers on either side (7-4-7), one of the 7's must be shaded.
- 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 (and cells on either side must be black). If one of the end numbers were white this would result in either two adjacent filled in cells or two white cells in the same row/column, neither of which are 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 either two adjacent filled in cells or two white cells in the same row/column, neither of which are 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.
Hitori is an original puzzle of Nikoli; it first appeared in Puzzle Communication Nikoli in issue #29 (March 1990).
- Episode 11 of xxxHolic: Kei is titled Hitori in reference to this.
- Puzzle Cyclopedia, Nikoli, 2004. ISBN.