Hitori

Hitori is a logic puzzle where the player starts with a grid completely filled with numbers. The goal is to shade certain cells so that no number appears more than once in any row or column. Shaded cells cannot be horizontally or vertically adjacent to each other, and all unshaded cells must form a single connected group. The name means "alone" or "single" in Japanese, referring to the requirement that each number must stand alone in its row and column.

Rules

1. The grid is pre-filled with numbers (typically NxN with values from 1 to N).
2. Shade cells to eliminate duplicates: no number may appear more than once in any row or column among the unshaded cells.
3. Shaded cells may not be adjacent horizontally or vertically (diagonal adjacency is allowed).
4. All unshaded cells must remain connected — you must be able to travel between any two unshaded cells through horizontally or vertically adjacent unshaded cells.

Strategies

• Unique Numbers: If a number appears only once in its row and column, it can never be shaded.
• Triple Rule: If three identical numbers are consecutive in a row or column, the middle one cannot be shaded (because shading either neighbor would force two adjacent shaded cells). So the outer two must be shaded.
• Sandwich Rule: If two identical numbers have one cell between them, and shading that middle cell would disconnect the grid or violate adjacency, you can determine which of the duplicates to shade.
• Adjacency Propagation: If you shade a cell, all four neighbors are confirmed unshaded. This often forces further deductions.
• Connectivity Check: Before shading a cell, consider whether it would disconnect the unshaded region. If removing it would split the white cells into separate groups, it must remain unshaded.
• Corner/Edge Logic: Cells in corners and edges have fewer neighbors, making adjacency and connectivity constraints more restrictive.

Hitori was first published by the Japanese puzzle company Nikoli, which has been one of the most prolific creators of logic puzzles since the 1980s. The puzzle appeared in Nikoli's puzzle magazines during the early 1990s.

The name "Hitori" comes from the Japanese word meaning "alone" or "single," reflecting the puzzle's core mechanic of ensuring each number stands alone (appears only once) in its row and column.

Like many Nikoli puzzles, Hitori follows the company's design philosophy of simple rules that produce complex logical challenges. The three constraints — no duplicate numbers, no adjacent shading, and connectivity — interact in subtle ways that require careful reasoning.

Hitori gained international recognition through puzzle competitions and online puzzle communities. It has been featured in the World Puzzle Championship multiple times. The puzzle's appeal lies in its unusual starting point — unlike most puzzles where you add information to an empty grid, Hitori begins fully filled and asks you to remove (shade) the excess.

The puzzle has been widely adopted in puzzle books and apps. Simon Tatham's Portable Puzzle Collection includes a Hitori implementation, and the puzzle appears regularly on online puzzle platforms. Its unique "subtractive" solving approach — starting from too much information and paring it down — gives it a distinctive feel among grid puzzles.