Hitori - Everything2.com

Hitori is a logic game by the same people who popularized Sudoku. The puzzle is a square grid of numbers, with each cell already containing a number. Just like in Sudoku, the numbers have to be unique per column and row. The puzzle is in the fact that the not all the numbers are unique, and you have to figure out which of the cells to 'paint' in so that there are no duplicates. The other two restriction are that no two painted cells may be touching horizontally or vertically, while all the unpainted (white) cells must be connected (so that you can get from any white cell to any other by only making vertical and horizontal moves).

Strategies

Although figuring out strategies and moves for games like this one seems like the only truly satisfactory endeavor, people are giving these away left and right, so I will too.

Notation made up by me, but I wouldn't mind if others used it or made up a better one

5 7 - cells which are yet determined as necessarily white or painted
{5 {7 - cells which must be left unpainted (circled¹)
#5 #7 - cells which must be painted (black)

1: when solving puzzles on paper, some prefer to circle the cells they know to be white. This is vital knowledge and must be kept track of, even in the digital world

Smart Moves

Since no two painted cells can be touching, once you determine one cell to be painted, you know all four cells touching it are white:
```
  5  6  9        5 {6  9  
  4 #8  7  -->  {4 #8 {7
  3  4  3        3 {4  3
```
Once one cell is determined to be white, all the other cells with that number in the column and row of the white cell can be painted. The point is to figure out which cells should be the unique, and once you did, you know the rest aren't (at least in that row or column):
```
  5  6  3  8 {5  3  1  5  -->  #5  6  3  8 {5  3  1 #5
```
If two cells with the same number in a row or column are touching, you know any other cells with that number in the row or column must be painted, since one of the two touching cells must be white (or the two cells would be both painted and touching, a no-no).
```
  5  8  3  8  8  3  1  8  -->   5 {8  3  8  8  3  1 {8
```
Of course, these hints alone assumes the oft-mentioned stratagem: If the same number appears three times consecutively, the middle one is circled and the surrounding two are painted:
```
  5  8  8  8  6  7  5  4  -->   5 #8 {8 #8  6  7  5  4
```
but this can be derived from the first three hints, since the first two 8's dictate the third one (going in either direction) should be painted (hint #3) and then the middle 8 should be white (hint #1), so the third 8 has to be painted, as it's in the same row (hint #2).
The above sub-hint can be generalized into a non-trivial form: any cell between two cells with the same number must be white, but you don't know as much about the surrounding cells:
```
  5  8  2  8  6  7  5  4  -->   5  8 {2  8  6  7  5  4
```
Any cell, that if painted, would isolate one group of white cells from the rest, must be white:
```
.--------        .--------   ;  
| 6 {7 #8        | 6 {7 #8   ;   {5 #6 {9       {5 #6 {9
|{4  6  9  -->   |{4 {6  9   ;   #4 {8 #7  -->  #4 {8 #7
|#3  2  7        |#3  2  7   ;   {3  4 {3       {3 {4 {3
```
In the first example the white cells would be cornered and in the second they would be encircled.
This hint can be used to guess which cell to paint when the previous hints can't help you any more:
```
.-----         .-----
| 2  2   -->   |#2 {2
| 2  2         |{2 #2
```
Since painting the other diagonal (they must be diagonal or they would touch) would isolate the 2 in the corner.