Shading grid · remove the duplicates

Hitori Puzzles

Shade cells out until no number appears twice unshaded in any row or column — without ever letting two shaded cells touch, and without cutting the rest of the grid into separate pieces. Tap once to shade, again to mark a cell as staying. Every grid has one answer and needs no guesswork.

Published by Nikoli as hitori ni shite kure — roughly, "leave me alone".

What Is Hitori?

Hitori hands you a grid already full of numbers and asks which of them to take away. Shade cells out until no number appears more than once unshaded in any row or column — and that would be a simple job, except that two further rules govern which cells you are allowed to shade.

Nikoli, the Japanese publisher that also popularised sudoku, prints it as hitori ni shite kure, which translates roughly as "leave me alone" — a fair description of what you are doing to the duplicates.

The Three Rules, And Which One Does The Work

What each rule forbids, and what you can deduce from it
RuleWhat it forbidsWhat it gives you
No repeatsThe same number twice unshaded in a row or columnThe goal itself — and once a cell is known to stay, every other copy in its lines is shaded.
No touchingTwo shaded cells sharing an edge (corners are fine)Every cell beside a shaded one is immediately known to stay.
Stay joinedShading that seals unshaded cells off from the restDecides corners and edges — the cell that cannot be shaded because of what it would cut off.

The third rule is what lifts hitori above a row-and-column exercise. Every other number grid on this site decides a cell from its own line; here, a cell in one corner can be settled by what shading it would do to the opposite corner. That is a genuinely different kind of reasoning, and it is why the solver had to learn about connectivity at all.

Three Of A Kind, And Where Else To Start

  1. Three of a kind in a line. The middle one stays; both outer ones are shaded. Shading the middle would leave two equal numbers unshaded in the same line, so it cannot be right.
  2. A touching pair. Two identical numbers side by side cannot both be shaded, so one survives — which means every other copy in that line must be shaded, before you know which of the pair it is.
  3. Mark what you keep. Shading a cell tells you its four neighbours stay. Marking them matters: a kept number is what forces its duplicates elsewhere to go.
  4. Test the corners. Ask of any cell you are about to shade whether it would seal anything off. If it would, it stays — regardless of the numbers.

Marking cells as kept is not optional. A player who only shades will stall. The duplicate rule fires from a cell that is known to stay — "this 4 is staying, so the other 4 in this row must go" — so leaving everything undecided leaves that rule with nothing to work from. Tapping a cell twice marks it kept.

Why These Grids Are About A Third Shaded

That figure is measured rather than chosen. A hitori is made by deciding the shading first and then choosing numbers to justify it — and below roughly a quarter of the grid shaded, the puzzles stop having single answers almost entirely:

Grids with exactly one answer, out of ten attempts at each setting
Shaded5×56×67×78×8
16%0000
20%0000
24%101050
28%10101010
32%10101010

The reason is the swap. A shaded cell duplicates one that stays, and unless something stops it, you could shade the other copy instead and be equally right. Only when the grid is crowded enough do the touching and connection rules block those swaps. So difficulty here comes from size rather than from thinning the shading, which would simply stop producing puzzles at all.

Hitori Puzzles Frequently Asked Questions

What is hitori?

A logic puzzle on a grid of numbers. You shade cells out until no number appears twice unshaded in any row or column — while never letting two shaded cells touch, and never cutting the unshaded cells into separate groups. Nikoli publishes it as hitori ni shite kure, roughly "leave me alone".

What are the three rules of hitori?

No number twice unshaded in any line. No two shaded cells sharing an edge — corners are fine. And every unshaded cell reachable from every other, moving only up, down, left or right.

What is the first move in hitori?

Find three identical numbers in a line: the middle stays, both outer ones go. Then look for a touching pair of equals — one of them must survive, so every other copy in that line is shaded.

Why do shaded cells have to stay apart?

It is a rule in its own right, and it does real work: every cell beside a shaded one is immediately known to stay, which often settles a duplicate elsewhere in that line without further reasoning.

What does the connection rule actually stop?

It stops a cell being shaded when doing so would seal off a group of unshaded cells — a corner cut away, for instance. It is what makes hitori more than a row-and-column puzzle: a cell on one side can be decided by what would happen on the other.

Is hitori like sudoku?

Only in using a grid of numbers. Sudoku asks you to place numbers; hitori gives you all of them and asks which to remove. And hitori has a rule about the shape of the whole grid, which nothing in sudoku resembles.

Does every puzzle here have one answer?

Yes, and it is checked rather than claimed. Every grid is verified to have exactly one valid shading, and separately verified to be solvable by reasoning alone.

What does hitori mean?

It is Japanese for "alone", and the full name is usually given as "leave me alone". It describes what you are doing to the grid: shading out the duplicate numbers until every one that is left stands alone in its row and column. Like most puzzles of this family it was popularised by the Japanese publisher Nikoli.