Masu PuzzleJapanese Logic Puzzles

Hitori techniques

ひとりにしてくれAlso called Hitori ni shite kure

Hitori looks like guesswork for about a minute. Then a handful of patterns start doing most of the work. Here they are, roughly in the order you’ll spot them.

In each picture, the cells the technique decides are outlined in blue.

  1. The sandwich

    313

    When a number sits between two copies of another number, like 3 1 3, the middle one stays unshaded. If you shaded it, neither 3 beside it could be shaded too (shaded cells can’t touch), so both 3s would stay and repeat. Circle the middle.

  2. Three in a row

    222

    Three copies side by side, like 2 2 2, settle all three cells: shade both ends and keep the middle. Shading the middle would leave both outer 2s stuck unshaded next to it.

  3. A pair and a loner

    4414

    If two copies sit side by side, at most one of them can be shaded, so one of the pair stays. Any other copy further along that row or column must be shaded.

  4. Circle around every shaded cell

    123221312

    Every neighbor of a shaded cell stays unshaded. Circle them straight away. Each new circle can force its twins in the same row and column to be shaded, which starts a chain.

  5. A circled number rules out its twins

    5253

    Once a number is circled, every other copy of it in the same row and column has to be shaded. Most of a solve is this step and the one above, taking turns.

  6. Never cut the board in two

    133321213

    Unshaded cells must stay connected, so a shade that would wall something off is never allowed. Corners are where this bites first: if one neighbor of a corner cell is shaded, the other neighbor must stay unshaded, or the corner would be cut off.

If you get stuck, look for a cell where shading it would break a rule two steps later: two shaded cells touching, a repeated circled number, or a cut-off area. That cell must stay unshaded.