THE THREE RULES
Hitori is played on a square grid pre-filled with numbers. Your goal is to shade some cells so that the following three conditions are all satisfied:
- No duplicates: no digit appears more than once in any row or column among the unshaded (white) cells.
- No adjacency: no two shaded cells may share an edge (diagonal adjacency is fine; only horizontal and vertical neighbours are forbidden).
- Connectivity: all unshaded cells must form one connected region — no isolated white islands.
The puzzle is already solved when you shade the exact cells that make all three conditions true simultaneously. There is always exactly one valid solution.
WHY THREE RULES CREATE SO MUCH COMPLEXITY
Each rule in isolation is easy to satisfy. The complexity comes from their interactions. Shade a cell to eliminate a duplicate in one row, and you may create an adjacency violation with a nearby shaded cell — forcing you to leave a cell white. But leaving that cell white might create a duplicate in a column. And shading the column duplicate might disconnect the white region.
This is Hitori's core dynamic: every shading decision is simultaneously constrained by all three rules, and shading one cell often forces a cascade of mandatory decisions in nearby cells. A good Hitori solve feels less like applying rules and more like following a chain of logical consequences.
Sudoku has three rules too (rows, columns, 3×3 boxes), but they're all the same type of constraint — no-duplicate. Hitori's three rules are different in kind: one removes duplicates, one constrains neighbours, one constrains global topology. The diversity is what makes them interact so richly.
THE SANDWICH PATTERN — WHERE TO START
The fastest entry into any Hitori grid is finding what solvers call the "sandwich pattern": when the same number appears three times consecutively in a row or column. The middle occurrence must be shaded (it's a duplicate of both neighbours), and because two shaded cells can't be adjacent, the two outer occurrences must be left white.
Example: a row contains …4, 4, 4… in positions 3, 4, 5. Position 4 must be shaded (duplicated on both sides). Positions 3 and 5 cannot both be shaded (adjacency violation with position 4's shade), so they stay white. Now the duplicates in their respective columns need to be resolved — which may force more shading decisions elsewhere.
The sandwich pattern is a forced deduction. Always find and resolve all sandwiches before doing anything else.
THE NO-TOUCH FORCE
The adjacency rule (rule 2) has an underrated positive form: if a cell is shaded, both its horizontal and vertical neighbours must be white. This often forces cells white that you wouldn't have known to leave white otherwise.
Once a cell is forced white, the no-duplicate rule (rule 1) may force its duplicate in the same row or column to be shaded. And that new shading forces its neighbours white again. The two rules feed each other: shade-forces-white, white-forces-shade.
Most Hitori deductions are actually this two-rule loop. You rarely need rule 3 (connectivity) to make progress — but connectivity guards are critical when you're considering whether to shade a cell that would cut the white region in two.
CONNECTIVITY LAST — BUT TAKE IT SERIOUSLY
The connectivity constraint (rule 3) is less immediately useful than the other two — it doesn't give you direct forcing moves the way sandwiches and no-touch do. But it prevents a lot of wrong shading decisions that would otherwise look legal.
Before shading any cell, ask: would this shading disconnect any part of the remaining white region? Specifically, cells in corners and edges are more likely to be connectivity-critical — shading an edge cell cuts off all the cells in the corner beyond it.
On hard Hitori grids, connectivity is where the final deductions live. Once you've applied sandwiches and the shade-forces-white loop as far as they go, the remaining ambiguous cells are usually resolved by asking "which of these two options disconnects the white region?" — and eliminating it.
THE SOLVE ORDER
- Find all sandwich triples (X, X, X in a row/column) — shade the middle, leave the two outer cells white.
- Apply no-touch: for every shaded cell, mark its four orthogonal neighbours as white.
- Apply no-duplicate: for each cell forced white in the previous step, find and shade the other occurrences of that digit in the same row and column.
- Repeat steps 2–3 until no new deductions emerge.
- Connectivity check: for any remaining ambiguous shading, test whether shading would disconnect the white region — if so, leave white.
Most beginner and medium Hitori grids solve completely in one or two passes through this loop without any guessing. On hard grids, you may need to consider pairs of ambiguous cells together.