Kakurasu Puzzle Generator
Kakurasu is the shading puzzle where position is value. The columns are worth 1, 2, 3 and so on from the left, and the rows are worth 1, 2, 3 and so on from the top. Shade squares so every row's shaded columns add up to the number beside it, and every column's shaded rows add up to the number underneath. Each grid here is checked to have one shading and no other.
What this generator does
Shades a grid at random, reads the row and column totals off it, then keeps the grid only when those totals lead back to that shading and no other.
How to use this tool
- Pick a grid size — six by six is a comfortable sitting.
- Choose how much of the answer is shaded, which changes the feel more than the difficulty.
- Print or copy the grid; the small numbers along the edges are the column and row weights.
- Shade squares until every total on the right and underneath is met exactly.
- Show the answer to check your shading.
Understanding the controls
- Grid
- Four to eight squares a side. Eight is the ceiling because proving a nine-by-nine unique takes over two seconds, which is too long to wait for a puzzle.
- Shading
- Roughly how much of the finished grid is shaded. Sparse grids have smaller totals and denser ones larger, which changes the arithmetic rather than the reasoning.
- Seed (optional)
- Type anything to rebuild the same puzzle later, which is how you reprint a page you have lost. Deterministic, not cryptographic.
Common use cases
- A short logic puzzle for a commute that needs no pencil marks
- Arithmetic practice where the sums come out of the layout rather than a worksheet
- A puzzle page for a newsletter or a club handout
- Something different for solvers who have had their fill of sudoku
- Reprinting the identical grid later from its seed
How this generator works
Uniqueness is proved from the printed numbers alone. Every row is expanded into the list of shadings that hit its own total, and those lists are combined a row at a time, abandoning any partial answer whose column running-total has already overshot or can no longer be reached. The search stops the moment it finds a second answer, and a grid with a second answer is thrown away rather than patched. The check shown under the puzzle repeats that solve from the totals on the page and compares it square by square with the answer.
Randomness and fairness
The shading, and therefore the totals, come from your browser's cryptographic random source unless you give a seed — a seeded puzzle is deterministic, not cryptographic.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The grid stops at eight squares a side, which is a measured limit rather than a preference.
- Difficulty is not graded. A grid with one answer can still need a long look at which column weights add to the total, and nothing here estimates that.
- Grids whose totals allow a second shading are discarded, so a dense eight-by-eight takes a moment.
- Totals of zero are possible on a sparse grid; a zero simply means nothing in that line is shaded.
Privacy and your data
The grid is built and checked entirely in your browser. Nothing you type as a seed, and no puzzle made from it, leaves the device.
Related generators
- Suguru Puzzle GeneratorPrints a Suguru — also called Tectonic — where each region holds 1 up to its size and no two equal numbers touch, with exactly one answer.
- Nonogram GeneratorPrintable nonograms whose clues are proved to have exactly one solution, and to be solvable without guessing.
- Kakuro GeneratorCross-sum puzzles where every run adds to its clue using distinct digits — every clue satisfiable by construction.
- Hitori Puzzle GeneratorShade out the repeats without letting two shaded cells touch or the rest come apart, with a single answer proved by construction and by search.
- Binary Puzzle GeneratorFill a grid with 0s and 1s: equal numbers in every row and column, never three in a row, no two lines alike.