Hitori

Pick a size and a level and a fresh board of numbers is built in your browser, checked, and put on screen. No limit, no account, nothing uploaded.

A puzzle where you take things away

The board arrives already full. Every cell holds a number and none of them will change; what you decide is which of them survive and which get painted out. That is the whole of the interaction, and it makes hitori the one puzzle on this site where you never write anything down — you are editing a grid rather than filling one.

Three conditions have to hold when you are finished. No number may appear twice among the survivors of any row or of any column. No two painted cells may touch along an edge. And everything still standing has to be joined into a single region, so that you could walk from any surviving number to any other without ever stepping on a painted cell.

The first condition tells you what to paint. The second and third tell you what you cannot paint, which is a stranger and much more interesting thing to be told. Most of the time on a hitori board you are not looking for the next cell to remove; you are working out which cell is now impossible to remove, and keeping it.

Three ways to mark a cell, and why the middle one matters

Tap a cell once to paint it out, again to mark it as one you intend to keep, and a third time to put it back to undecided. Two of those three states are what the answer is made of. The third is what the reasoning is made of.

Marking a cell as kept places nothing and removes nothing, which is exactly why people skip it — and skipping it is the commonest reason a hitori board feels stuck. A cell you have decided to keep paints out every twin of its number along its row and its column, and it is one of the cells the connectedness argument counts. If that decision only lives in your head, you will make it again ten minutes later, and the argument that depended on it will be invisible.

The keyboard does the same three things. Arrow keys move, X paints a cell out, K keeps it, space cycles through all three and backspace returns a cell to undecided. On paper the equivalent is a dot in the corner, and the good solvers all use one.

What separates an easy board from a hard one

Not the size of the board. A 10×10 with plenty of repeated numbers is a long puzzle rather than a hard one — it asks the same two questions forty times. The levels name the argument a board forces on you instead, and every one of them is measured rather than estimated.

Easy is finished by reading the printed numbers and following the consequences: twins side by side, a number caught between two of its own, and then the cascade of what each decision forces. Medium adds the corner argument, where painting a cell would seal two or three numbers off from everything else. Hard is the same argument on a pocket too big to recognise at a glance. Expert is the point where painting a cell would divide the whole board in half, which is something you can only find by tracing.

Every published board is solved by a program that always takes the cheapest argument that fits, and the hardest one it was ever cornered into is the level printed on the board. A board built for one level that turns out to need another ships under the level it measured. That is occasionally disappointing and it is always honest.

Common questions

More Hitori pages

• Daily hitoriA new board every day
• Hitori rulesThree rules, in full
• Solving a boardA 6×6, worked
• Hitori techniquesThe whole ladder
• Printed patternsTechnique — the opening
• Following throughTechnique — easy
• Corners and edgesTechnique — medium
• Sealed pocketsTechnique — hard
• Cutting the boardTechnique — expert
• Guessing at hitoriTechnique — refused
• Printable hitoriFor paper
• Hitori archiveEvery past board