Rules
Kakurasu is a shading puzzle. Every cell is shaded or empty. The number left of a row is the sum of the shaded cells in that row. A shaded cell adds the weight printed under its column, counting 1 from the left. The number above a column is the sum of the shaded cells in that column. A shaded cell adds the weight printed to the right of its row, counting 1 from the top. Empty cells add nothing.
The numbers on the right and along the bottom are those weights, not extra sums. The corners stay empty. A 5×5 uses weights 1 through 5, and the full sum is 15. The daily puzzle is a 6×6 and uses weights 1 through 6. Play runs from 5×5 to 9×9. 5×5 is easy or medium. 6×6 through 9×9 are easy, medium, or hard. No cell starts shaded or crossed. The grid is finished when every cell is marked, every row matches the sum on its left, and every column matches the sum above it.
Kakuro is the familiar part: a sum has to be hit. Kakuro places digits in a run, and a digit cannot repeat. Kakurasu shades a cell or crosses it. The same column weighs a different number in a row than that row weighs in a column.
- Shade or cross. Every cell is shaded or empty. A shaded cell counts. An empty cell adds nothing. Nothing starts filled in.
- Row sums use the bottom weights. The number left of a row is the sum of its shaded cells. A shaded cell adds the weight under its column, counting 1 from the left.
- Column sums use the side weights. The number above a column is the sum of its shaded cells. A shaded cell adds the weight beside its row, counting 1 from the top.
- Finished. The grid is done when every cell is marked, every row matches the sum on its left, and every column matches the sum above it.
The 0 left of row 3 has five crosses. The 15 left of row 5 is shaded all the way across. The shaded cell in row 2, column 4 adds 4 in that row, because it sits under the weight 4. In the column it adds 2, because it sits in row 2. Shades, crosses, sums, weights, and the frame are teal.
- Shade
- Cross
- Weight
- Sum met
- Sum clashes
Choose Shade or Cross. Tap a cell, or drag across cells. The first cell decides: the mark already there clears it, and the drag follows. Tap a cell that already has the mark to clear it. With a mouse, right-click places a cross, or clears a cross that is already there. Arrow keys move and stop at the edge. S or 1 shades. E, X, or 2 crosses. Backspace, Delete, or 0 clears the cell. Space or Enter places the selected mark, or clears it when the cell already has that mark.
Selecting a cell tints its row and column, lights the sums at the ends of that row and that column, and turns the weight beside the row and the weight under the column violet. A sum turns teal when the shaded weight already matches it, even if cells are still open. A sum of 0 stays plain on a line you have not marked, until you mark that line or every cell on it is empty. A sum turns red when the shaded weight has gone past it, or when the cells still open cannot reach it. The cells on that line take a red wash. The weights on the right and the bottom do not turn red.
Press Hint for one step the rules already force, with a sentence saying why. Hint lights the cells it writes and the sums it uses. Press Check when you want the board checked. Undo and Redo step through the moves. Reset clears the grid. When every cell is shaded or empty and those marks are the solution, the board turns teal: shades, crosses, sums, weights, and frame.
The line under the tools reads "Tap a cell, or drag across cells, to place the mark. Tap a mark again to clear it. With a mouse, right-click crosses." Solved, that line and the dialog body read "Every shaded cell matches the row and column sums." The dialog title is "Solved!"
- Shade
- Cross
- Undo
- Redo
- Reset
- Hint
- Check
One line
Read one sum at a time. A 0 clears a line. The full sum shades a line. The other three sentences are still that one line.
A sum of 0 Easy
A sum of 0 means nothing on that line is shaded. Cross every open cell. On this grid one row is 0, so the press crosses that row and stops. If two lines are 0, one press crosses both. One 5×5 easy grid crosses two rows together. This picture has one. The other sums do not have to be filled in first. This is the first press on the blank 5×5 in this section.
The 0 sits left of row 3. Every weight is at least 1, so the only way to add to 0 is to shade nothing. The row is still entirely open. All five cells are ringed, and each new cross is ink on the wash. No other row is washed. Hint says "This line is 0, so every open cell on it is empty."
The next press on this board is the full sum. It is the second press, not a second zero.
The full sum Easy
A sum that equals 1 + 2 + … + n sees every weight, so every open cell on that line is shaded. On a 5×5 that sum is 15. Hint shades the whole line in one press. It does not stop after the first cell. A full column would shade from top to bottom in the same kind of press. This grid's full line is a row, and it is the second press, after the zero row is crossed. Another 5×5 opens on the same sentence, with no cross already on the board. That shaded row is the setup for the later sections. It is not a second picture.
The weights under the columns are 1, 2, 3, 4, and 5. They add to 15, so every one of them has to be shaded. Crossing any one of them would leave at most 14. The five cells of row 5 are ringed. Each is a new shade. The teal crosses on row 3 stay, and that row is not washed. The 15 is lit. Hint says "This line is the full index sum, so every open cell on it is shaded."
One fitting weight Easy
Look at the weights that are still open. If only one of them equals the sum still needed, shade that cell and cross the other open cells on the line. The crossed cells are part of the same press. Their weights are not the one that fits. This needs a second open cell. A line with a single cell left is the next section or the one after it, not this one. The blank 5×5 above does not say this. One 5×5 easy grid does, as a later press. This figure is the blank board that opens on it.
The open weights are 1, 2, 3, 4, and 5. The sum still needed is 1. Only the first weight equals 1. The cell under column 1 is shaded, and the other four cells of the row are crossed in the same press so they cannot be added later. All five cells are ringed. The 1 is lit. Hint says "Only one open weight equals the sum still needed, so that cell is shaded and the other open cells on the line are empty."
Too big Easy
An open weight larger than the sum still needed cannot be shaded. Cross it. On this figure the row is still empty, the sum is 4, and the weight under column 5 is 5, so that cell is crossed. One press can cross every too-big cell on the board. This grid has only one. The usual press does not fill the cell with a shade.
When the shaded cells already add up to the clue, the remainder is 0, so every open weight is too big. The how-to calls that "already enough." Hint uses this same sentence. On the first grid, the last press does that: row 1 is already 4 from the shade in column 4, and the press crosses the two cells still open. That second picture is not drawn.
Row 1 is already the full sum, shaded in ink. Row 3 still needs 4, and the row is otherwise open. Weight 5 is larger than 4. Weights 1, 2, 3, and 4 are not, so they stay open. Only the cell under column 5 is ringed. The rest of the row is not washed. The 4 is lit. Hint says "Open weights larger than the sum still needed are empty."
Cannot skip Easy
Cover the sum with the open weights. If leaving one of them out would make the line short, that cell has to be shaded. On this figure the row adds to 15 if every cell is shaded, and the clue is 11. Leaving out the 5 leaves at most 10, so the cell under column 5 is shaded. Leaving out the 4 leaves 11, so that cell is not forced. One press can shade every such cell. This grid has only one.
When the open weights add up to exactly what is left, every one of them is required. The how-to calls that "the rest of the line." Hint uses this same sentence.
Row 1 is still the full sum. The cross under column 5 of row 3 is the previous press, and row 4 does not use it. The open weights on row 4 are 1, 2, 3, 4, and 5, and they add to 15. The clue is 11. 15 − 5 = 10, which is short of 11. 15 − 4 = 11, which still meets the clue, so weight 4 stays open. Only the new shade is ringed. The 11 is lit. Hint says "The line cannot reach its clue without these cells, so they are shaded."
That is the end of the easy sentences. An easy grid finishes with these, and not every grid uses each one. One 5×5 easy grid uses a sum of 0, the full sum, and one fitting weight. It never says too big or cannot skip. The next section is medium. A medium grid still opens with an easy sentence when one applies. The grid in the last two pictures opens on the full sum.
More than one way
When a single weight is not forced, list the ways one line can still add up. A hard grid may have to try those ways against the other sums.
Ways one line can add Medium
List the ways the open weights on one line can still add up to what is left. A cell that is shaded in every remaining way is shaded. A cell that is in none of them is crossed. The other lines are not part of this list. The figure crosses one weight, because that weight is in neither remaining way. It does not fill the cells that belong to only one of the ways. This is a medium sentence. On the state below, an easy setting returns no hint.
Row 1 is the full sum. Column 5 already holds a shade in row 2, the too-big cross in row 3, a shade in row 4, and a cross in row 5. Row 3's clue is 4, and column 5 is already crossed, so the open weights are 1, 2, 3, and 4. The ways to make 4 are 1+3, and 4 alone. Weight 2 is in neither way. Weight 1 is only in the first. Weight 3 is only in the first. Weight 4 is only in the second. The press crosses the 2 and leaves the other three open. Only that cell is ringed. The 4 is lit. Hint says "Every way to make this line's sum agrees on the open cells it fills."
That is the end of the medium sentence. Hard grids add a look that tries one line's ways against the other sums. A hard grid does not have to use this list. One 6×6 hard grid never says it.
What still fits Hard
Pick a line that still has only a few ways to make its sum. Write each way in turn, and run the easier steps on the rest of the grid. A cell that comes out the same in every way that still fits is the one to mark. The cell does not have to sit on the line you tried. This figure tries row 2, which can make 8 in five ways, and the cell that comes out shaded is in row 7. The other cells do not come out the same, so the press writes one cell. This needs the hard setting. On the blank board, easy and medium return no hint.
The five ways on row 2 are 1+3+4, 1+2+5, 3+5, 2+6, and 1+7. All five still fit the other sums. All five shade the cell in row 7, column 6. Hint tries this row first because it is tied for the fewest ways, and a row is tried before a column.
The board is blank. Row 2 is the line with five ways. Each way was written, and the easier steps were run on the rest of the grid. None of the five broke another sum. The only unknown cell they agree on is row 7, column 6, and they shade it. Only that cell is ringed. Row 2 is a lit clue, not a row of rings. The sum of row 7 and the sum above column 6 light as well. The press does not claim those sums are finished. Hint says "Every completion of this line that still fits the other clues agrees on these cells."
That is the end of the hard sentence the grids here use. A hard grid uses this look when the easier sentences are not enough. It does not have to use the one-line list first. The one-cell try is the next section, and it was not a press on these grids.
What if
When the deductions above have not written a mark, the last step tries one open cell both ways. It looks at cells in the end columns before cells in the middle. Shade is tried, and empty is tried. Each try is followed only by the one-line steps, not by another look across lines and not by another try. If one of the two marks breaks a sum, the other mark is written. Hint says "The other mark contradicts the clues, so this mark stays." It does not name the mark that failed. The picture would show the mark that stays, and only that cell.
If both marks still fit, Hint tries a different cell. It looks at most at eight cells in one press. If both marks break, the grid is already broken and Hint has nothing to write. There is no second result where both marks force the same cells.
This step is in Hint. It was not the next press on the grids here, including the hard ones. The look those hard grids do use is the section above. A 5×5 has no hard setting. Do not go there for this step.
Common mistakes
Check marks a sum when the shaded weight has gone past it, or when the open cells can no longer reach it. The cells on that line take a red wash. A line that can still reach its sum is not a mistake yet. A shade that simply is not the solution, and breaks nothing, stays quiet. A sum can turn teal because the shaded weight matches, while those shades are still the wrong cells. Check does not compare the line with the answer.
Hint, on the play page, refuses while Check would fail. The toast is "This board has a mistake, so there is no hint yet." The pictures of broken boards show the coral marks and no amber ring. A shade that breaks nothing shows the ink shade and the amber hint, on a different row. All of these pictures are the same 5×5 as the rules. Row 1's solution is a shade only in column 4, and that weight is 4, which matches the clue of 4. Row 3's clue is 0. Row 5's clue is 15. Column 1's clue is 5, and the solution shades only row 5 there.
The cell under column 5 is shaded. Its weight is 5, and the clue is 4. The clue turns coral, and the row takes the red wash. The shade uses that line's colour. No amber ring. Hint refuses until the shade is gone. A shade on the zero row is not quiet either. One shaded cell in row 3 puts that row over its 0, and Hint refuses in the same way.
Rows 2 and 4 are shaded in column 1. In the column those are weights 2 and 4, and 2 + 4 = 6. The clue above the column is 5, so that clue turns coral and the column takes the wash. Both shades use the line colour. Row 2's clue is 14 and row 4's clue is 5, so neither row is over from a single weight of 1. No amber ring. Hint refuses.
Row 5's clue is 15. The first cell is crossed, and the other four are still open, so the most the row can add is 14. The 15 turns coral. The row takes the wash, and the cross is coral. No amber ring. Hint refuses. The cross stays until you clear it.
A shade in the first cell is weight 1, and the row clue is 4, so the line is not over. The solution wanted this cell empty. The shade stays ink. No coral. The amber ring is the opening sum of 0, on row 3, with crosses ready to write. If Hint runs, it crosses that row and leaves the shade where it is.
Row 1 is shaded in columns 1 and 3. 1 + 3 = 4, which is the clue, so the 4 turns teal. The solution cell, column 4, is still open. Check does not compare the row with the answer. Both shades stay ink. No coral. The amber ring is still the sum of 0 on row 3. After that press, both shades are still there.
What to play next
An easy grid finishes with a sum of 0, the full sum, one weight that fits, a weight that is too big, or a cell the line cannot skip. A medium grid adds the ways one line can still add up, and it can open on an easy sentence. A hard grid tries one line's ways against the other sums. The one-cell try is there when a grid still has not broken, and the grids here finish before it. The boards above are teaching boards.
- EasyOne line at a timeA sum of 0, the full sum, one weight that fits, a weight that is too big, or a cell the line cannot skip. Every easy grid here has a 0 and a full sum. Not every easy grid says the other three.Play 5×5 Easy →Play 6×6 Easy →
- MediumWays one line can addThose, and the ways one line can still add up. A medium grid can open on an easy sentence.Play 5×5 Medium →
- HardWhat still fitsA line's ways tried against the other sums. Not every hard grid uses the one-line list first. The one-cell try is there for a grid that still has not broken, and the grids here finish before it.Play 6×6 Hard →Play 7×7 Hard →
5×5 comes in easy and medium. 6×6 through 9×9 come in easy, medium, and hard. The daily puzzle is a 6×6 easy grid: today's Kakurasu and 6×6 easy. A new player can start on a 5×5 easy grid, or on the daily.
Print a Kakurasu pack. A single pack has eight puzzles. The starter pack has seventeen, one of every size and setting, including print-only 10×10. Four 5×5, 6×6, or 7×7 grids share a sheet. Two 8×8, 9×9, or 10×10 grids share a sheet. Large print is one grid. The pages are black and white. Sums and weights print. Answer pages fill the shaded cells and leave the empty cells blank. Amber, red, teal, and crosses do not print.
Kakuro fills digits in a run. Nonograms read shaded runs. Binairo marks every cell one of two ways.
- GuideKakuroKakuro fills digits in a run. A digit cannot repeat.
- GuideNonogramsThe clues are shaded runs.
- GuideBinairoEvery cell is one of two marks.
- GuideSudokuEach digit once in every row, column and box.
- GuideHashiCount bridges, never cross, connect every island.
- GuideStar BattleOne or two stars in every row, column and region.
- GuideSlitherlinkDraw one loop. Start from the 0s and the 3s.
- GuideHitoriShade repeats, never side by side, keep white connected.
- GuideNurikabeGrow each island to its number and keep one sea.
- GuideLight UpLight every cell. Start beside the 4s and 0s.
- GuideKiller SudokuCage sums, then the rest of the line.
- GuideJigsaw SudokuFollow the thick walls. Each region has its own shape.
- GuideFutoshikiLess-than and greater-than signs between neighbours.
- GuideRenzokuDots between cells. An empty gap means not one apart.
- GuideSkyscrapersEach clue counts the heights it can see.
- GuideCalcudokuOne-way cages first, then the rest of the line.
- GuideShikakuEach number is an area. Start with the ones that fit one way.
- GuideMasyuTurn on black pearls, go straight through white ones.