Hitori Puzzle Maker

How to solve it

Shade cells out until three things are true at once. No number appears twice unshaded in any row or column. No two shaded cells touch edge to edge. And every unshaded cell is still reachable from every other, so the board is never cut into islands. The second and third rules are what make it a puzzle rather than a crossing-out exercise — you often prove a cell must stay showing because shading it would strand a corner.

⭐There is a floor, and below it a Hitori is not a puzzle

A sparse board looks like an easy board. It is not an easy board — it is usually not a board at all, because it has many answers rather than one. Building grids at a fixed share of cells shaded, 120 per measurement, and counting how many turned out to have exactly one solution:

At 22% shaded and below, not one grid of 120 had a single answer — and that is true at every size tested, not just the small one. Eight percentage points later most of them do. It is a cliff rather than a slope, which is the part worth knowing: there is no gentle region of "slightly ambiguous" boards to tune into. A board is either above the floor or it is not a puzzle.

The reason is that shading is only ever forced by a duplicate. A cell whose number already appears nowhere else in its row or column has no reason to be shaded — but no rule forbids shading it either, so long as it touches nothing shaded and strands nothing. Every such free cell doubles the number of answers. Only once the board carries enough duplicates does the no-touching rule bite hard enough to pin those cells down.

One assumption worth recording as wrong: I expected a bigger board to need proportionally more shading, the way most grid puzzles get harder to pin down as they grow. It does not. The floor sits at the same share of cells for 6 × 6, 8 × 8 and 10 × 10 — so what matters is the fraction shaded, not the count, and a 10 × 10 is no harder to make well-posed than a 6 × 6.

Which leaves a narrow window to aim at

The floor is not the only wall. The no-touching rule caps how much of a board can be shaded at all: shaded cells must form an independent set, so however greedily you shade, the board saturates around 31%. Between a floor at 22% and a ceiling at 31%, the entire usable range for a well-posed Hitori is about 9 percentage points wide. Every puzzle printed here is generated inside that window and then checked — the solver counts answers and stops at two, because two is all a uniqueness check ever needs to find, and only boards with exactly one are shown.

⚠️Honest limits: 120 boards per measurement, one generator, one way of choosing which duplicates to plant. The floor is a property of these boards; the mechanism above is the reason to expect it generally, not the sample size. The 8 × 8 and 10 × 10 columns are measured once and frozen into the page rather than recomputed on every build — the sparse rows are the slow ones, because proving a board has a second answer means going and finding it — and the test suite re-derives them at full sample so they cannot drift.