The full logical solve of the hard Kakuro for September 29 to October 5, 2026, 12 × 12. 84 steps, 5 techniques, no guessing. Step through it, or jump to any step below.
The across 4 has 2 cells, and only 1 + 3 makes 4 with different digits. The down 3 has 2 cells, and only 1 + 2 makes 3 with different digits. 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 across 3 has 2 cells, and only 1 + 2 makes 3 with different digits. 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 down 8 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The across 15 can only use 6 to 9, and the down 7 can only use 1 to 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 15 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
The down 13 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
The down 7 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 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: 7.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The down 17 has 2 cells, and only 8 + 9 makes 17 with different digits. The across 9 can only use 1 to 8, and the down 17 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 9 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 12 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The down 13 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
The across 15 can only use 1, 2, 4 and 5, and the down 22 can only use 5 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 15 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The down 11 has 4 cells, and only 1 + 2 + 3 + 5 makes 11 with different digits. The across 14 can only use 5, 6, 8 and 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 14 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
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 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: 7.
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 2. That leaves the marked cell with one digit: 2.
The down 3 has 2 cells, and only 1 + 2 makes 3 with different digits. The across 11 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.
The across 11 has one empty cell left, and the run still needs 9. 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.
This takes 11 steps in the highlighted runs. The last two: The across 12 can only use 3, 4, 5, 7, 8 and 9, and the down 7 can only use 1 to 6. The outlined cell sits in both, so it needs a digit from both lists. In the across 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: 7.
Its across and down runs already use every digit but 5, so the marked cell is 5.
This takes 3 steps in the highlighted runs. The last two: The across 35 has 5 cells, and only 5 + 6 + 7 + 8 + 9 makes 35 with different digits. The down 7 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The across 11 has one empty cell left, and the run still needs 9. That leaves the marked cell with one digit: 9.
The down 8 has one empty cell left, and the run still needs 1. That leaves the marked cell with one digit: 1.
The across 8 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
This takes 26 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 across 14, only 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: 8.
Its across and down runs already use every digit but 6, so the marked cell is 6.
The down 12 still needs 6 from 3 cells, and only 1 + 2 + 3 does it. The down 21 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.
This takes 7 steps in the highlighted runs. The last two: In the across 12, 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 11, only 2 + 4 + 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: 2.
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 4, so the marked cell is 4.
In the across 27, 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. 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.
Its across and down runs already use every digit but 8, so the marked cell is 8.
The across 18 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.
The across 27 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
This takes 6 steps in the highlighted runs. The last two: In the down 5, 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 29, 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 11 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.
In the across 14, only 2 + 5 + 7 or 1 + 5 + 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: 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 5, so the marked cell is 5.
The down 8 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The across 9 has one empty cell left, and the run still needs 6. 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.
The across 12 has one empty cell left, and the run still needs 3. That leaves the marked cell with one digit: 3.
The across 6 can only use 1, 2, 4 and 5, and the down 15 can only use 4, 5, 7 and 8. 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 15 has one empty cell left, and the run still needs 8. That leaves the marked cell with one digit: 8.
The down 24 has one empty cell left, and the run still needs 6. That leaves the marked cell with one digit: 6.
In the across 18, only 1 + 2 + 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: 4.
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 14 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.
The down 5 has one empty cell left, and the run still needs 1. 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.
This takes 3 steps in the highlighted runs. The last two: In the down 13, only 5 + 7 or 3 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. In the across 25, only 5 + 7 + 8 or 3 + 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: 8.
Its across and down runs already use every digit but 9, so the marked cell is 9.
The across 21 still needs 7 from 2 cells, and only 2 + 5 does it. That leaves the marked cell with one digit: 5.
Its across and down runs already use every digit but 2, so the marked cell is 2.
The down 13 has one empty cell left, and the run still needs 7. That leaves the marked cell with one digit: 7.
The across 25 has one empty cell left, and the run still needs 5. That leaves the marked cell with one digit: 5.
This takes 4 steps in the highlighted runs. The last two: In the across 22, only 3 + 5 + 7 or 2 + 4 + 9 still fit the digits these cells can hold, which rules digits out of the orange cells. In the down 17, only 2 + 6 + 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: 6.
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 5, so the marked cell is 5.
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 2, so the marked cell is 2.
The across 12 has one empty cell left, and the run still needs 2. That leaves the marked cell with one digit: 2.
The across 22 has one empty cell left, and the run still needs 4. That leaves the marked cell with one digit: 4.