The full logical solve of the hard Kakuro for September 22 to September 28, 2026, 12 × 12. 81 steps, 5 techniques, no guessing. Step through it, or jump to any step below.
The across 17 has 2 cells, and only 8 + 9 makes 17 with different digits. 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 12 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The down 16 has 2 cells, and only 7 + 9 makes 16 with different digits. The across 8 can only use 1, 2, 3, 5, 6 and 7, 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 8 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 16 has 2 cells, and only 7 + 9 makes 16 with different digits. The across 16 can only use 7 and 9, and the down 14 can only use 5, 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: 9.
Its across and down runs already use every digit but 7, so the marked cell is 7.
The down 14 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 9 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The down 17 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
This takes 21 steps in the highlighted runs. The last two: In the down 12, only 5 + 7 or 4 + 8 still fit the digits these cells can hold, which rules digits out of the orange cells. In the across 19, only 5 + 6 + 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: 6.
This takes 4 steps in the highlighted runs. The last two: The across 17 has 2 cells, and only 8 + 9 makes 17 with different digits. The down 15 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
The across 13 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The down 12 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 5, so the marked cell is 5.
The down 14 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
This takes 47 steps in the highlighted runs. The last two: In the across 16, 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 5 + 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: 5.
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 9, so the marked cell is 9.
The across 6 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 16 still needs 6 from 2 cells, and only 2 + 4 does it. 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 8 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
The down 8 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: The across 32 can only use 3, 5, 6, 7, 8 and 9, so the outlined cell in it can only hold those digits. The across 32 can only use 3, 5, 6, 7, 8 and 9, and the down 4 can only use 1 and 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.
This takes 8 steps in the highlighted runs. The last two: In the across 16, only 1 + 2 + 6 + 7 still fits the digits these cells can hold, which rules digits out of the orange cells. In the down 8, only 1 + 2 + 5 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.
The across 20 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 7, so the marked cell is 7.
Its across and down runs already use every digit but 6, so the marked cell is 6.
The down 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.
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 across 10 can only use 1 to 4, and the down 29 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.
This takes 3 steps in the highlighted runs. The last two: In the across 11, only 3 + 8 or 2 + 9 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: 5.
The across 33 still needs 28 from 4 cells, and only 4 + 7 + 8 + 9 does it. In the across 33, 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: 4.
This takes 5 steps in the highlighted runs. The last two: In the across 9, 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 7, only 3 + 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: 3.
Its across and down runs already use every digit but 4, so the marked cell is 4.
The across 32 still needs 14 from 3 cells, and only 1 + 6 + 7 does it. 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 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 6, so the marked cell is 6.
Its across and down runs already use every digit but 3, so the marked cell is 3.
The across 11 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 32 can only use 6, 8 and 9, and the down 23 can only use 3, 5, 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.
The down 23 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The across 13 can only use 2, 4, 5 and 7, and the down 33 can only use 3 to 9. The outlined cell sits in both, so it needs a digit from both lists. In the down 19, only 2 + 4 + 6 + 7 or 1 + 4 + 6 + 8 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.
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 4, so the marked cell is 4.
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 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 down 19 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 5 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The down 33 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
This takes 5 steps in the highlighted runs. The last two: In the down 8, only 3 + 5 or 2 + 6 still fit the digits these cells can hold, which rules digits out of the orange cells. 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. That leaves the marked cell with one digit: 1.
This takes 4 steps in the highlighted runs. The last two: In the across 9, 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 37, 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: 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.
The down 16 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
The across 26 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The down 8 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
The across 9 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The down 37 still needs 17 from 3 cells, and only 4 + 6 + 7 does it. That leaves the marked cell with one digit: 4.
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 7, so the marked cell is 7.
The across 8 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The across 11 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
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 8 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
The across 9 still needs 4 from 2 cells, and only 1 + 3 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.
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.