Play Kuromasu Online
Place black cells so each numbered clue sees the correct count of white cells in all four directions. No two black cells may touch, and all white cells must stay connected.
Created by Brian Hamilton
Tap a cell to shade it black — tap again to clear
How to play Kuromasu
Shade some squares black. Each numbered square is white, and its number is how many squares it can see — itself included — looking up, down, left and right until a black square blocks the view.
- No two black squares may touch edge to edge.
- All white squares must form one connected group.
- A numbered square is never black.
- Every puzzle has exactly one solution.
Controls: tap a square to mark it black, tap again to mark it white, and a third time to clear it.
The number counts a cross, not a region
The commonest misreading of Kuromasu is treating a number like a region size, the way Nurikabe or Shikaku would. It is not. A Kuromasu number counts what its square can see: itself, plus every white square in a straight line up, down, left and right, stopping at the first black square in each direction.
The useful consequence is arithmetic. A clue's number is (its clear run across) + (its clear run down) − 1, subtracting one because it counts itself in both. Once you think of it that way, every clue becomes a statement about two line segments rather than a blob, and the two can be reasoned about separately.
Both ends of the range are gifts
The most a square can ever see is its whole row plus its whole column, which on an n×n grid is 2n − 1 — 13 on a 7×7, 27 on a 14×14. A clue at that maximum is the strongest thing on the board: its entire row and column must be white, settling up to 2n − 1 squares at a stroke.
Small numbers are just as informative in reverse. A clue of 2 sees only itself and one neighbour, so every direction but one is blocked immediately — three black neighbours for a square in the middle of the grid, two for one against an edge, since the edge blocks the view for free. And because black squares may not touch, each of those blacks then forces white squares diagonally around it.
| Clue | 2–3 | 4–6 | 7–9 | 10+ | At the max 2n−1 |
|---|---|---|---|---|---|
| Share | 16% | 34% | 15% | 35% | 2.4% |
No clue stands alone
The single most useful structural fact about these boards is that clues are never isolated.
Across those 72 boards, every clue shared a row or a column with at least one other clue — 100% of them. That means any clue you look at is being constrained by a second one, and the pair almost always says more together than either does alone.
Two clues in the same row are the case worth learning. Their horizontal runs either overlap or they do not, and whichever it is, the black squares that separate them are pinned down fast. If both can see each other, every square between them is white and both counts include that whole stretch; if their numbers are too small for that, a black square must sit between them, and there are usually very few places it can go.
A worked board
Only about 18% of the grid ends up black. That is worth holding in mind: most squares are white, so the productive question is usually "where must the few blacks go?" rather than trying to prove squares white one at a time.
Where solvers get stuck
Forgetting that black squares cannot touch. Every black square you place makes its four neighbours white for free. That rule does as much work as the numbers.
Ignoring connectivity until the end. All white squares must form one group, so a black square that would seal a white square into a pocket is wrong even when every count still works. This is the most common way a nearly-finished board turns out to be incorrect.
Counting only one direction. A clue constrains its row and its column simultaneously, and it is easy to satisfy one while quietly breaking the other. When you place a black square, re-check every clue that can see along that line — often several.
Two things you can check about these puzzles
Every puzzle has exactly one solution. This was not previously true: measured against an exhaustive counter, only 11 of 40 boards had a single solution, and 7×7 Hard had none at all. The generator now starts with every white square numbered and removes clues one at a time, keeping a removal only when a solver confirms exactly one solution still remains. 56 boards across every size and difficulty were then re-checked against a separate counter written from the rules alone; all 56 were unique.
Difficulty is how many numbers are left. Easy keeps about 47% of the squares numbered, Medium 34% and Hard 25%. Removal cannot go much below that last figure — strip more and the board stops having a single answer — so Hard is close to the sparsest a Kuromasu board can honestly be.
Kuromasu, Kurodoko and Where is Black Cells
Kuromasu is Nikoli's, and appears as Kurodoko and under the wonderfully blunt translation Where is Black Cells. It shares its two structural rules — no two black squares touching, all white squares connected — with Nurikabe and Heyawake, which is why the endgame feels familiar if you have played those.
What makes it its own puzzle is the line of sight. Nurikabe's numbers describe a shape you build around them; Kuromasu's describe a distance you can see. That turns the whole board into a set of interlocking row and column measurements, and it is the reason a single large number can settle a quarter of the grid.
More shading puzzles
If you like deciding which squares to blacken, try these: