Hitori

Hitori - a logic puzzle

Hitori is another logic puzzle with numbers like Sudoku. There is also some information on Hitori - Wikipedia.

A Hirori puzzle is a grid of squares which are filled with numbers. At the beginning all numbers are not marked. The goal of the game is to paint out some numbers to fulfill the following three basic rules:

• Two black cells cannot be connected horizontal or vertical. Diagonal is allowed.
• In each row and each column of the grid no white duplicate numbers are allowed.
• All white cells needs to be connected orthogonally at the end. Diagonal is not enough.

Example puzzle	Solution

Explaination of rules
Not allowed: orthogonal pair of black numbers	Mark all neighbours of a black cell as white
Not allowed: duplicate white number in one row	If one number is white, paint black all other numbers in the same row/column
The number between two duplicates (sandwich position) cannot be white, because then both duplicates would need to be white!	A number in sandwich position needs to be white
Not allowed: area of white cells is separated from the others with a wall of black cells	A number in a corner which is surounded by duplicates needs to be black
If a corner contains a pair of duplicate numbers the other number in the corner cannot be black, because in this case the corner cell will be separated from the other cells	In case of duplicates in a corner the third cell needs to be white.
In this case the white "1" needs to be connected to the rest of the grid	The "3" is the only possible expansion position and needs to be white (Single Expansion in corner)
In this case the white "1" needs to be connected to the rest of the grid	The "3" is the only possible expansion position and needs to be white
In this case the 2 cells are already black	The cell on the orange postion needs to be white, because otherwise the left upper corner will be separated