How to Solve Hitori Puzzles

How to play on this site

Tap a square to shade it. Tap it again to circle it, which is your note for "this one stays white", and a third tap clears it. If you would rather circle first, the options swap the order. Press and drag to paint the same mark across a run of squares, which is handy for circling a whole row of safe digits at once.

On a keyboard, the arrow keys move the cursor and Space or Enter cycles the square. S or X shades it straight away, C or O circles it, Backspace clears it and U (or Ctrl and Z) undoes your last change. Undo and Clear sit under the grid too.

With mistakes shown (an option you can turn off), the page marks repeated digits among the white squares, shaded squares side by side, and white squares cut off from the rest. Easy grids are 5 × 5, medium 7 × 7 and hard 9 × 9. Your time ranks you, and fewer changes break a tie.

Find the conflicts first

Before shading anything, look for the digits that repeat in their row or column. Those are the only squares a rule can force into the shade, because a square is shaded when its twin has to stay white. A digit that appears only once is not shaded by any twin. The rules do allow shading it, but in the one answer it stays white, because it touches a shaded square or holds the white squares together. Leave those for later; the other rules will settle them.

A circle is more useful than it looks. Once a square is circled, any other copy of the same digit in its row or column must be shaded, because two white copies would be twins. Circling and shading feed each other through the whole solve.

The a b a sandwich

When a digit sits between two copies of another digit, like 3 5 3 in a row, the middle square must stay white. Here is why: one of the two 3s has to be shaded (they are twins), and whichever it is touches the 5. If the 5 were shaded too, two shaded squares would touch side by side. So circle the 5.

The sandwich works in columns as well, and it is the commonest opening move on medium and hard grids. Scan every row and column for it before you do anything clever.

Pairs side by side

When two equal digits sit next to each other, like 4 4, one of them must be shaded and the other must stay white, because they are twins but cannot both be shaded. You don't know yet which is which, but you do know something about every other 4 in that line: none of them can stay white, since one of the pair already does. Shade them all.

This is a strong move. In a row like 4 4 2 4, the last 4 is shaded at once, which circles its neighbours, which can settle the pair in turn.

The neighbours of a shaded square

Every time you shade a square, circle its neighbours above, below, left and right. They cannot be shaded, because shaded squares never touch. Those new circles then shade the twins of their own digits, and the solve snowballs. Keep this habit up and most easy grids fall apart without a single hard decision.

Keep the white squares joined

The joining rule is the one most solvers forget, and it is often what finishes a hard grid. Look at a square you are thinking about shading and ask: would its shading cut a white square, or a whole pocket of white squares, off from the rest? If so, it must stay white.

Corners and edges are where this bites. A corner square has only two neighbours. If one is already shaded, shading the other would trap the corner, so the other must stay white. The same thing happens along an edge when two shaded squares close in on a square from both sides. In the middle of the grid, watch for a diagonal chain of shaded squares that is about to close into a wall.

When you get stuck

Hard grids sometimes need one step of looking ahead. Pick an undecided square and imagine it shaded. Circle its neighbours, shade the twins of those circles and keep following the plain rules for a step or two. If that leads straight to a broken rule (two twins left white, two shaded squares touching, or a pocket cut off), the square must stay white instead. Then try the same with the square circled.

Choose the square well: one whose digit has only two copies in its line, near an edge or beside other decided squares, gives quick answers. A square in the open middle of the grid rarely tells you anything.

A worked opening

Take a 5 × 5 row reading 2 1 2 3 2. The middle 2 sits between a 1 and a 3, so the sandwich rule doesn't help there, but the 1 sits between two 2s: circle the 1. The 3 sits between two 2s as well: circle it. Now the 2s are the only conflict in the row. They sit in squares one, three and five, so no two of them touch, and exactly one of them stays white. Look at their columns. As soon as a column rule circles one of the three 2s, the other two are shaded at once. If instead a column shades one of them, the other two are still twins, so keep looking down their columns for the next clue. That cross check between a row and the columns it meets is the heart of every Hitori solve.

Daily play

There is a new grid at each difficulty every day, the same for everyone, and your first solve of the day is ranked. Start with easy if you are new: the sandwiches and the neighbours of shaded squares finish it. Medium grids lean on pairs, and hard grids need the joining rule and the odd look ahead.

If you enjoy shading and circling, try Light Up, Futoshiki and Skyscrapers next.