To solve Hitori without guessing, you need a short list of moves and the habit of applying them in the same order each time. This page teaches how to solve Hitori with five such moves, then applies them to a real 6 x 6 grid from the LogikLand generator, square by square. If you do not know the three rules yet, read Hitori rules first.
Before you start
Work in pencil, and use two marks: a circle for a square you know stays white, and a filled square (or a cross) for a square you know is shaded. The important point is that every mark must come from a reason. In LogikLand books a grid is only kept if it can be solved by reasoning of exactly this kind, so a square that "looks right" is never needed.
A method in five moves
- Circle the lonely numbers. A number that appears only once in its row and once in its column has no copy to remove, so it stays white.
- Read the sandwiches. In a pattern like 5 3 5 in a row, one of the two 5s must be shaded. If the 3 between them were shaded too, two shaded squares would touch. So the middle square is white.
- Read the pairs and triples. Two equal numbers side by side cannot both be shaded (they would touch) and cannot both stay white (same number). Exactly one of them is white, so any third copy in that row or column is shaded. Three equal numbers in a row are a triple: the two outer ones are shaded and the middle one is white.
- Spread the consequences. A shaded square makes its four neighbours white. A circled square makes every other copy of its number in its row and its column shaded.
- Check the connection. Before you shade a square, ask whether it would close off a white square or a group of white squares. If so, it stays white.
Moves 1 to 4 solve the easy and medium grids of the LogikLand assistant. Move 5 matters from the hard level on, where at least one square needs the "connected" rule.
Solving a 6 x 6 grid
This is a medium grid. Rows are counted from the top and columns from the left, starting at 1. The solution is drawn on the right so you can follow along.
Move 1: a lonely number
The 2 in the top-left corner is alone: row 1 is 2, 3, 6, 4, 4, 1 and column 1 is 2, 6, 4, 5, 6, 1, with a single 2 in each. Circle it. This move gives you the first white squares and several of them in each pass.
Move 3: a triple
Row 4 reads 5, 2, 2, 2, 1, 3. Three 2s in a row make a triple. Shade the 2nd and the 4th squares of the row and circle the 3rd one.
Move 4: spread what you know
- The circled 2 in row 4, column 3 has other 2s in its column: column 3 reads 6, 3, 2, 2, 4, 2 from top to bottom. The 2s in rows 3 and 6 are shaded.
- The 2 in row 4, column 4 is shaded, so the three squares around it (row 3 column 4, row 5 column 4, row 4 column 5) are white. The shaded 2 in row 6, column 3 makes the squares on both of its sides white (row 6, columns 2 and 4).
- The 2 in row 6, column 2 is now circled. Another 2 sits in column 2, in row 2: shade it. In the same way the 4 in row 6, column 4 is circled, so the 4 in the top row, column 4 is shaded.
Each of these marks has a reason you can write next to it. After a few more passes of moves 3 and 4, every square is decided. This grid never needed move 5: you can check that no square had to be left white only because shading it would cut the white region.
Tip
Work one pass at a time. Scan the whole grid for moves 1 to 3, then spread the consequences, then scan again. New circles and new shaded squares keep appearing for four more passes in this grid.
When you are stuck
If no move applies, go through this short list before you give up:
| Look for | What it tells you |
|---|---|
| A white square whose other neighbours are all shaded | Its last neighbour cannot be shaded |
| A corner square with one neighbour shaded | The other neighbour must stay white, or the corner is cut off |
| A number that appears in a row with a circled copy | All its other copies in that row are shaded |
| A chain of shaded squares touching at corners | Do not close it into a loop: it would enclose white squares |
In LogikLand, hard grids need the connection check at least once and expert grids at least three times, so this list is where those solutions come from. The article on advanced Hitori techniques works through a real 8 x 8 example.
Checking your answer
When every square is decided, run the three rules once more. Read each row and each column and make sure no number repeats among the white squares. Look at each shaded square and confirm that no neighbour above, below, left or right is shaded. Last, trace a path through the white squares from one corner to the other without lifting your pencil. In a LogikLand book, compare with the solutions pages, where shaded squares are dark grey.
Where to practise
The quickest practice is a set of small grids. Try printable easy Hitori puzzles, then move up to 6 x 6. To make your own book, create a free account to make a full book: the Hitori assistant offers the four levels, from 5 x 5 to 9 x 9.
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