The full logical solve of the hard Kakuro for September 1 to September 7, 2026, 12 × 12. 81 steps, 5 techniques, no guessing. Step through it, or jump to any step below.
The down 16 has 5 cells, and only 1 + 2 + 3 + 4 + 6 makes 16 with different digits. The across 14 can only use 5, 6, 8 and 9, and the down 16 can only use 1, 2, 3, 4 and 6. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 6.
The across 14 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
The down 10 has 4 cells, and only 1 + 2 + 3 + 4 makes 10 with different digits. The across 13 can only use 4 to 9, and the down 10 can only use 1 to 4. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 4.
The across 13 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
This takes 70 steps in the highlighted runs. The last two: In the down 25, only 3 + 6 + 7 + 9, 3 + 5 + 8 + 9 or 1 + 7 + 8 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 13, only 2 + 5 + 6 or 1 + 5 + 7 still fit the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 5.
The across 14 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
In the across 15, only 7 + 8 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 8.
Its across and down runs already use every digit but 7, so the marked cell is 7.
The down 13 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 23 can only use 5 to 9, and the down 10 can only use 1 to 7. The outlined cell sits in both, so it needs a digit from both lists. In the across 23, only 6 + 7 + 9 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 9.
The down 12 still needs 3 from 2 cells, and only 1 + 2 does it. In the across 12, only 1 + 2 + 9 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 9.
The down 15 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
The across 8 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 2, so the marked cell is 2.
Its across and down runs already use every digit but 1, so the marked cell is 1.
This takes 6 steps in the highlighted runs. The last two: In the across 8, try each set of digits in each cell. Some digits have no cell left that can hold them in any set, so they come out of the orange cells. In the down 25, only 1 + 7 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 7.
Its across and down runs already use every digit but 6, so the marked cell is 6.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The down 10 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
In the down 28, only 4 + 7 + 9 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 4.
The across 6 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The across 11 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
Its across and down runs already use every digit but 9, so the marked cell is 9.
This takes 4 steps in the highlighted runs. The last two: In the across 19, only 2 + 4 + 5 + 7, 2 + 3 + 6 + 7 or 2 + 3 + 5 + 8 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 6, only 2 + 4 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 2.
Its across and down runs already use every digit but 4, so the marked cell is 4.
Its across and down runs already use every digit but 5, so the marked cell is 5.
The down 7 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
This takes 11 steps in the highlighted runs. The last two: In the down 19, try each set of digits in each cell. Some digits have no cell left that can hold them in any set, so they come out of the orange cells. In the down 14, only 1 + 5 + 8 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 1.
Its across and down runs already use every digit but 5, so the marked cell is 5.
Its across and down runs already use every digit but 8, so the marked cell is 8.
The across 8 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The across 14 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
The down 12 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
This takes 12 steps in the highlighted runs. The last two: In the across 14, only 2 + 3 + 4 + 5, 1 + 3 + 4 + 6 or 1 + 2 + 5 + 6 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 10, try each set of digits in each cell. Some digits have no cell left that can hold them in any set, so they come out of the orange cells. That leaves the marked cell with one digit: 3.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 2, so the marked cell is 2.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 2, so the marked cell is 2.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The down 21 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
This takes 3 steps in the highlighted runs. The last two: In the across 10, only 4 + 6, 3 + 7 or 2 + 8 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 7, only 1 + 6 still fits the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 6.
Its across and down runs already use every digit but 1, so the marked cell is 1.
Its across and down runs already use every digit but 2, so the marked cell is 2.
The across 14 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 19 still needs 16 from 2 cells, and only 7 + 9 does it. That leaves the marked cell with one digit: 7.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 10 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The across 19 can only use 3, 5, 7 and 9, and the down 33 can only use 3 to 9. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 5.
The across 19 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
The down 33 still needs 28 from 4 cells, and only 4 + 7 + 8 + 9 does it. That leaves the marked cell with one digit: 4.
The across 5 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
This takes 5 steps in the highlighted runs. The last two: In the down 15, try each set of digits in each cell. Some digits have no cell left that can hold them in any set, so they come out of the orange cells. In the across 16, only 3 + 6 + 7 or 1 + 6 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. That leaves the marked cell with one digit: 6.
The down 15 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
Its across and down runs already use every digit but 8, so the marked cell is 8.
The across 15 can only use 3, 4, 5, 7, 8 and 9, and the down 16 can only use 1, 2, 3, 5, 6 and 7. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 7.
The across 15 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The down 17 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
Its across and down runs already use every digit but 8, so the marked cell is 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
Its across and down runs already use every digit but 7, so the marked cell is 7.
Its across and down runs already use every digit but 8, so the marked cell is 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
Its across and down runs already use every digit but 7, so the marked cell is 7.
Its across and down runs already use every digit but 6, so the marked cell is 6.
Its across and down runs already use every digit but 8, so the marked cell is 8.
Its across and down runs already use every digit but 6, so the marked cell is 6.
The across 13 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The down 12 still needs 8 from 2 cells, and only 2 + 6 does it. That leaves the marked cell with one digit: 2.
Its across and down runs already use every digit but 6, so the marked cell is 6.
The across 8 still needs 6 from 2 cells, and only 1 + 5 does it. That leaves the marked cell with one digit: 1.
Its across and down runs already use every digit but 5, so the marked cell is 5.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The across 19 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 16 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 16 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.