How to solve Hitori

What is Hitori?

Hitori is a Japanese logic puzzle first published by Nikoli around 1990. The name means "alone" (ひとり) — a reference to the goal of making each number stand alone in its row and column. You start with an N×N grid filled with numbers 1 through N. Some numbers appear more than once in the same row or column. Your job is to shade cells black until every row and column has no duplicate unshaded numbers.

The catch is that shading is constrained. You cannot shade two adjacent cells, and all the unshaded cells must form one connected group. These three rules interact in ways that make even small grids surprisingly engaging.

The three rules

1. No duplicate white numbers: In every row and every column, no number may appear more than once among unshaded (white) cells. If a row has two 4s, at least one of them must be shaded black.
2. No adjacent blacks: No two black cells may share an edge — horizontally or vertically. Diagonal touching is fine. This prevents you from shading too aggressively.
3. White connectivity: All unshaded (white) cells must form a single connected group. You should be able to travel from any white cell to any other white cell by moving through orthogonally adjacent white cells. No islands allowed.

That's it. No arithmetic, no region constraints. Just three rules about shading and connectivity.

Worked example: 5×5 grid

Suppose row 1 contains: 3, 1, 3, 5, 2. The number 3 appears twice (cells 1 and 3). At least one of them needs to be shaded.

Step 1 — Sandwich rule. Cell 2 (holding 1) sits between the two 3s. The "sandwich" pattern means cell 2 must stay white — if the surrounding 3s are the only duplicates, we know shading decisions affect cells 1 and 3, but cell 2 is safe.

Step 2 — Adjacent rule. Look at column 1. If another cell in column 1 also needs shading, check whether shading cell 1 would put two black cells next to each other. If it would, cell 3 must be shaded instead.

Step 3 — Connectivity check. After shading cell 3, trace a path through all white cells. If every white cell is reachable from any other, the shading is valid. If not, undo and try the other option.

This is the core loop: find duplicates, apply sandwich and adjacency logic, then verify connectivity. Repeat until the grid is fully resolved.

Solving strategies

Sandwich rule

When a cell appears between two copies of the same number in a row or column (like 4-X-4), the cell X must stay white. This is the first technique to check because it gives free information without any risk.

Adjacent rule

If a number appears as a duplicate and one copy is next to an already-shaded cell, that copy must stay white (shading it would create adjacent blacks). The other copy must be shaded instead. Always check adjacency before committing to a shading decision.

Unique number rule

If a number appears only once in both its row and its column, it can never be the source of a duplicate violation. Mark it white immediately. On larger grids, scanning for unique numbers first provides a foundation of certainty.

Forced black

If a number appears as a duplicate in its row or column and every other copy is already white, this copy must be shaded. This comes up frequently mid-solve as other deductions lock cells into their white state.

Connectivity reasoning

On expert and einstein grids, you will encounter situations where shading a cell would cut the white cells into separate groups. Visualize each shading decision before committing — if it creates an island of isolated white cells, that cell must stay white regardless of duplicates.

What-if analysis

When direct techniques stall: pick an ambiguous cell, assume it's black, and follow the consequences. If you reach a contradiction (adjacent blacks, disconnected whites, or unsolvable duplicates), the cell must be white. On hard grids, one-step lookahead is usually enough. Einstein grids rarely require deeper than two steps.

Difficulty levels

ThePuzzleLabs Hitori comes in five difficulty levels that differ primarily by grid size:

• Easy (5×5): Sandwich rule and basic adjacency handle almost everything. Good for learning.
• Medium (7×7): Connectivity starts mattering. You will need to track which cells are safe to shade.
• Hard (9×9): Multi-step deductions and occasional what-if reasoning. Matches Sudoku grid size.
• Expert (12×12): 144 cells with complex interaction chains. Connectivity becomes a primary concern.
• Einstein (15×15): 225 cells, solvable by constraint propagation alone. The logic path exists but finding it is the challenge.

Hitori vs other puzzles

Unlike Sudoku, where you place missing numbers into a grid, Hitori starts with a full grid and asks you to remove numbers by shading. This reversal creates a different solving rhythm — you are eliminating rather than constructing.

Binairo shares the binary cell-state concept (in binairo: 0 or 1; in Hitori: black or white), but binairo has no connectivity constraint and uses counting rules instead. Star Battle uses three cell states (empty, star, eliminated) with adjacency constraints, making it a close cousin in terms of solving feel. If you enjoy Hitori, these are natural next puzzles to explore.

Common mistakes

Ignoring connectivity until the end. The biggest trap. Check connectivity as you shade, not after. On larger grids, an early shading mistake can create an island that is hard to detect until much later.

Shading too aggressively. When a number has three or four copies in a row, the instinct is to shade all but one immediately. But the adjacency rule may prevent certain combinations. Work through the implications before committing.

Missing the sandwich pattern. A cell sandwiched between two identical numbers must stay white. This is free information that many solvers overlook, especially when the identical numbers are spread across a long row.

Frequently asked questions