The full logical solve of the hard Kakuro for September 15 to September 21, 2026, 12 × 12. 80 steps, 5 techniques, no guessing. Step through it, or jump to any step below.
The down 23 has 3 cells, and only 6 + 8 + 9 makes 23 with different digits. The across 8 can only use 1, 2, 3, 5, 6 and 7, and the down 23 can only use 6, 8 and 9. 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 8 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The across 17 has 2 cells, and only 8 + 9 makes 17 with different digits. The across 17 can only use 8 and 9, and the down 9 can only use 1 to 8. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The down 9 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 17 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.
This takes 24 steps in the highlighted runs. The last two: The across 19 can only use 2 to 9, and the down 6 can only use 1, 2, 4 and 5. The outlined cell sits in both, so it needs a digit from both lists. The across 11 can only use 1 to 8, and the down 23 can only use 8 and 9. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 21 can only use 4 to 9, and the down 5 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 down 5 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
This takes 14 steps in the highlighted runs. The last two: The across 9 can only use 1 to 8, and the down 13 can only use 1 to 7. The outlined cell sits in both, so it needs a digit from both lists. The across 19 can only use 2 to 9, and the down 3 can only use 1 and 2. The outlined cell sits in both, so it needs a digit from both lists. 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.
This takes 6 steps in the highlighted runs. The last two: The down 5 can only use 1 to 4, so the outlined cell in it can only hold those digits. The across 22 can only use 1, 2, 3, 4, 5 and 7, and the down 15 can only use 6 to 9. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 7.
The down 15 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
This takes 26 steps in the highlighted runs. The last two: In the down 13, 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 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: 4.
Its across and down runs already use every digit but 2, so the marked cell is 2.
This takes 4 steps in the highlighted runs. The last two: In the across 17, 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 13, only 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: 5.
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.
In the down 9, only 2 + 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: 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 7, so the marked cell is 7.
The across 17 still needs 9 from 3 cells, and only 2 + 3 + 4 does it. In the across 17, 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: 2.
The down 18 still needs 16 from 2 cells, and only 7 + 9 does it. 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 7, so the marked cell is 7.
The across 9 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The down 12 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The down 34 still needs 21 from 3 cells, and only 6 + 7 + 8 does it. That leaves the marked cell with one digit: 6.
The across 7 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 6 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 12 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 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 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 8, so the marked cell is 8.
Its across and down runs already use every digit but 7, so the marked cell is 7.
The down 24 still needs 15 from 2 cells, and only 6 + 9 does it. That leaves the marked cell with one digit: 6.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 30 still needs 7 from 3 cells, and only 1 + 2 + 4 does it. That leaves the marked cell with one digit: 1.
Its across and down runs already use every digit but 3, so the marked cell is 3.
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 4, so the marked cell is 4.
The across 26 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
This takes 16 steps in the highlighted runs. The last two: In the across 31, 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 13, only 4 + 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.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 24 still needs 7 from 3 cells, and only 1 + 2 + 4 does it. In the across 24, 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: 2.
The across 22 can only use 1, 2, 3 and 5, and the down 15 can only use 4 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.
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.
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.
Its across and down runs already use every digit but 1, so the marked cell is 1.
The down 16 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 down 13 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
The down 11 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 down 10 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
In the down 34, only 1 + 4 + 5 + 7 + 8 + 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: 7.
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 22 still needs 6 from 3 cells, and only 1 + 2 + 3 does it. That leaves the marked cell with one digit: 3.
The down 5 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.
The down 8 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
The across 15 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 15 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
The down 5 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The across 31 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The across 6 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.