The full logical solve of the hard Kakuro for September 8 to September 14, 2026, 12 × 12. 84 steps, 5 techniques, no guessing. Step through it, or jump to any step below.
The down 11 has 4 cells, and only 1 + 2 + 3 + 5 makes 11 with different digits. The across 22 can only use 5 to 9, and the down 11 can only use 1, 2, 3 and 5. 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 22 still needs 17 from 2 cells, and only 8 + 9 does it. The down 16 has 2 cells, and only 7 + 9 makes 16 with different digits. That leaves the marked cell with one digit: 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.
The across 5 can only use 1 to 4, and the down 28 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: 4.
The across 5 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 16 has 2 cells, and only 7 + 9 makes 16 with different digits. The across 14 can only use 5, 6, 8 and 9, and the down 16 can only use 7 and 9. The outlined cell sits in both, so it needs a digit from both lists. That leaves the marked cell with one digit: 9.
Its across and down runs already use every digit but 7, so the marked cell is 7.
The across 14 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 6 can only use 1, 2, 4 and 5, and the down 25 can only use 3, 4, 7, 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: 4.
The across 6 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The down 25 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 7, so the marked cell is 7.
The down 16 has 2 cells, and only 7 + 9 makes 16 with different digits. That leaves the marked cell with one digit: 9.
Its across and down runs already use every digit but 7, so the marked cell is 7.
The across 3 has 2 cells, and only 1 + 2 makes 3 with different digits. The across 3 can only use 1 and 2, and the down 26 can only use 2 to 9. 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.
The across 20 still needs 4 from 2 cells, and only 1 + 3 does it. 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.
The down 16 has 2 cells, and only 7 + 9 makes 16 with different digits. The across 11 can only use 1 to 8, and the down 16 can only use 7 and 9. The outlined cell sits in both, so it needs a digit from both lists. 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 4 has 2 cells, and only 1 + 3 makes 4 with different digits. The across 4 can only use 1 and 3, and the down 19 can only use 2 to 9. The outlined cell sits in both, so it needs a digit from both lists. 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.
The down 5 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The across 27 still needs 23 from 3 cells, and only 6 + 8 + 9 does it. The down 19 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 7, so the marked cell is 7.
This takes 10 steps in the highlighted runs. The last two: The down 17 has 2 cells, and only 8 + 9 makes 17 with different digits. The down 26 still needs 24 from 3 cells, and only 7 + 8 + 9 does it. That leaves the marked cell with one digit: 8.
Its across and down runs already use every digit but 6, so the marked cell is 6.
The down 25 still needs 15 from 2 cells, and only 7 + 8 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.
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.
The down 11 has 4 cells, and only 1 + 2 + 3 + 5 makes 11 with different digits. The across 13 can only use 4 to 9, and the down 11 can only use 1, 2, 3 and 5. 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 13 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
This takes 24 steps in the highlighted runs. The last two: The across 33 can only use 3 to 8, and the down 18 can only use 1 to 7. The outlined cell sits in both, so it needs a digit from both lists. The across 33 can only use 3 to 8, and the down 11 can only use 1 to 3. The outlined cell sits in both, so it needs a digit from both lists. 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 3, so the marked cell is 3.
The across 33 still needs 21 from 3 cells, and only 6 + 7 + 8 does it. The down 18 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
This takes 7 steps in the highlighted runs. The last two: In the across 27, 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 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 7, so the marked cell is 7.
This takes 6 steps in the highlighted runs. The last two: In the across 20, 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 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. That leaves the marked cell with one digit: 1.
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 7, only 3 + 4 or 1 + 6 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 11, 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.
In the across 23, only 3 + 5 + 6 or 1 + 4 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 19, only 1 + 4 + 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: 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 1, so the marked cell is 1.
The across 7 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The across 23 still needs 10 from 2 cells, and only 1 + 9 does it. That leaves the marked cell with one digit: 9.
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 7 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
This takes 8 steps in the highlighted runs. The last two: In the across 25, 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 26, only 4 + 6 + 7 + 9 or 2 + 7 + 8 + 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: 9.
This takes 8 steps in the highlighted runs. The last two: In the across 7, 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 12, only 4 + 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.
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 4, so the marked cell is 4.
The down 26 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The across 15 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 5, so the marked cell is 5.
The across 20 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
This takes 3 steps in the highlighted runs. The last two: In the across 7, only 2 + 5 or 1 + 6 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 25, 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: 7.
This takes 3 steps in the highlighted runs. The last two: In the down 19, only 4 + 5 + 7, 3 + 5 + 8 or 3 + 4 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. In the across 23, only 3 + 4 + 7 + 9 or 1 + 6 + 7 + 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: 9.
Its across and down runs already use every digit but 8, so the marked cell is 8.
The across 13 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 25 can only use 1, 3, 4, 5, 6, 8 and 9, and the down 19 can only use 3, 4, 7 and 8. The outlined cell sits in both, so it needs a digit from both lists. In the across 25, only 4 + 5 + 9 or 1 + 8 + 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: 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.
The down 25 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 7 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
This takes 3 steps in the highlighted runs. The last two: In the across 14, 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 18, only 4 + 6 + 8 or 4 + 5 + 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: 4.
The across 23 can only use 2, 3, 7 and 8, 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.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The down 15 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
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 18 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
The across 27 still needs 12 from 2 cells, and only 3 + 9 does it. That leaves the marked cell with one digit: 3.
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 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 down 19 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
The across 25 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.