THE THREE RULES — AND HOW THEY INTERACT
Rule 1 (no-repeat): shade cells so no digit appears twice in any row or column.
Rule 2 (no-touch): shaded cells can't share an edge.
Rule 3 (connectivity): all unshaded cells must form one connected region.
Alone, each rule is straightforward. Together, they create a cascade: shading one cell (Rule 1) forces its four neighbours to stay unshaded (Rule 2), which can lock in rows and columns for unshaded cells, which can prevent shading elsewhere needed to fix a different duplicate (Rule 1 again), which reveals the forced shading — a different cell in that run.
This is the loop. Hitori is solved by triggering it and following where it leads.
START WITH DUPLICATES
Find every digit that appears twice or more in a single row or column. At least one instance must be shaded. You won't always know which one yet — but you know the set.
The easiest starting cells: digits that appear three times in a row. The middle cell of a run like 5 − 5 − 5 can't be the shaded one (shading it leaves both outer 5s as duplicates). If the two outer 5s are adjacent, you have even tighter constraints. Work these first.
Also look for a digit that appears twice in a row AND twice in the same column. Those intersections constrain both dimensions at once.
USE THE NO-TOUCH RULE AS A TOOL
Most beginners treat Rule 2 (shaded cells can't touch) as a constraint that stops them shading. Experienced solvers treat it as a source of information that tells them cells are safe to keep unshaded.
The moment you shade a cell, all four of its orthogonal neighbours are confirmed unshaded. Mark them immediately. A confirmed-unshaded cell that still has a duplicate in its row or column forces the shade to land on the OTHER duplicate instance — often a single logical step that cascades several more.
Think of confirmed-unshaded cells as "anchors". Every anchor you establish shrinks the space of possible shadings toward one solution.
THE SANDWICH PATTERN
If the same digit appears in adjacent cells with the same digit somewhere else in the row (X — X — ... — X pattern), the middle cell of the adjacent pair is safe. Shading either adjacent X would leave the other as a row duplicate — so the fix must shade the distant X instead.
More generally: any time only one possible shading avoids the no-touch rule AND fixes the duplicate, that shading is forced. Don't enumerate possibilities; look for the configuration where there's only one way out.
CHECK CONNECTIVITY LAST
Rule 3 (connectivity) is rarely your starting point — there are usually no isolated islands until the grid is mostly resolved. Use it as a final filter: before committing a shade, scan whether it would cut the unshaded region into two disconnected pieces.
Look especially at corners and narrow corridors. A pending shade that sits at the only bridge between two halves of the grid is almost always wrong — the puzzle has a unique solution and connectivity must hold everywhere.
On harder Hitori puzzles, connectivity becomes a positive deduction: if the only way to keep the grid connected requires a specific cell to stay unshaded, that cell is safe — and its duplicate must be the one to go.
THE SOLVING LOOP
Repeat until solved:
- Find the most constrained duplicate — triple runs, cross-axis duplicates, adjacent pairs.
- Shade the forced cell (or the only viable candidate).
- Mark all four neighbours as confirmed unshaded.
- For each newly confirmed-unshaded cell: does fixing its row/column duplicate become forced? If yes, shade that cell and repeat from step 3.
- Check connectivity if a shade would isolate a region.
- Go back to step 1 with the new information.
If you genuinely cannot find a forced move, you've either missed a duplicate or skipped a no-touch propagation. There's no guessing in a well-formed Hitori — the logic is always there.