THE THREE RULES — QUICK REFERENCE
- No duplicates: no digit can appear more than once in any row or column (shade extras until one remains).
- No touching shaded cells: shaded cells can never share an edge (horizontal or vertical).
- Connected whites: all unshaded cells must form a single connected group.
Rule 1 tells you what to shade. Rule 2 tells you what can't be shaded. Rule 3 stops you from over-shading. Apply them in that order.
STEP 1 — SCAN FOR DUPLICATE PAIRS
Find every digit that appears more than once in a row or column. At least one of each pair must be shaded. This is your starting material — don't shade yet, just mark the candidates.
Why not shade immediately? Because you don't know which of the pair gets shaded. Mark both as candidates and let the other rules decide.
STEP 2 — THREE IN A ROW FORCES THE MIDDLE
If the same digit appears three (or more) times in a row or column, the middle cell is always safe.
Why: if the middle were shaded, it would be adjacent to at least one of the outer copies — but the outer copies can't both be shaded either (no-touch), so one of the outer cells must stay unshaded. With the middle also unshaded, you still have two copies in the row. Either way the middle works out to safe.
More practically: three in a row means the two outer cells are the shade candidates, the middle is guaranteed white. Mark it safe immediately.
STEP 3 — NO-TOUCH FORCES SAFE NEIGHBOURS
Once you shade a cell, its four neighbours are all forced white. Mark them safe. If any of those white neighbours are duplicate candidates, the OTHER copy of the duplicate is now forced to be shaded.
Example: shade a cell at row 3, column 4. The cells at (3,3), (3,5), (2,4), and (4,4) are all forced white. If (3,3) was a duplicate candidate, the duplicate in its row or column is now forced shaded.
This cascade is how Hitori puzzles unravel. Each shade forces safe neighbours, which force new shades, which force more safe neighbours.
STEP 4 — CONNECTIVITY GUARD
Before shading a cell, ask: would this shade disconnect any white cell from the rest? If yes, you can't shade it — and by elimination, the other copy of its duplicate must be the shaded one.
Connectivity is best checked at bridge points — cells where a single white square is the only path between two groups. Never shade a bridge unless you can verify another route exists.
Tip: corner and edge cells are connectivity-sensitive. A shaded corner can only disconnect what's behind it; a shaded interior cell can disconnect in four directions.
THE SOLVING LOOP
- Scan each row and column, mark all duplicate candidates.
- Apply the three-in-a-row rule — mark middle cells safe.
- Shade any cell that is the only remaining candidate for its row/column duplicate.
- Mark all four neighbours of each new shade as safe.
- Check whether any newly-safe cell forces its duplicate to be shaded.
- Connectivity check before every uncertain shade.
- Repeat from step 3 until solved.
Hitori puzzles are designed to be solvable without guessing. If you feel stuck, an unapplied no-touch implication or a connectivity constraint is hiding somewhere in your current state.
THE BEGINNER TRAP
Shading both cells of a duplicate when only one is correct. The no-touch rule kicks in and forces the adjacent cells safe — which then creates new connectivity problems. If you notice two shaded cells touching, one of those shades was wrong. Undo back to the last certain move.
Hitori doesn't require trial and error. Every shade has a logical reason. If you can't state why a cell is shaded, treat it as uncertain and look for a different move.