Some sums allow one set
Each kakuro run holds different digits from 1 to 9 that add up to its clue. Some clues allow only one set of digits. Where two runs cross, the shared cell must hold a digit that is in both sets.
In the drawing, Across 4 has two cells. Two different digits that add up to 4 can only be 1 and 3, because 2 and 2 repeat a digit. Down 7 has three cells, and its only set is 1, 2 and 4.
The top left white cell is in both runs. Of 1 and 3, only 1 is also in 1, 2 and 4, so that cell is 1.
Look for these sums at the low and the high end. For two cells, the sums with one set are 3 (1 and 2), 4 (1 and 3), 16 (7 and 9) and 17 (8 and 9). For three cells, they are 6 (1, 2 and 3), 7 (1, 2 and 4), 23 (6, 8 and 9) and 24 (7, 8 and 9).
A set tells you which digits a run uses, not their order. The crossing runs decide which cell takes which digit.
Never repeat a digit in a run
A common slip is to make 4 out of 2 and 2. Down 7 can hold a 2, so the top left cell would seem to take one, and nothing looks wrong yet.
But a run never repeats a digit, so 2 and 2 is not allowed. Follow the slip and it breaks: Across 3 would need 1 first and 2 after it, and Down 6 would hold two 2s.
With the right sets, the board fills from the crossing, one cell at a time.
- The top left cell is 1, the only digit in both sets.
- Across 4 is 1 and 3, so its second cell is 3.
- Down 7 still needs 2 and 4. Across 3 is 1 and 2, so the first cell of Across 3 is 2.
- Down 7 now holds 1 and 2, so its last cell is 4.
- Across 3 already holds 2, so its second cell is 1.
- Down 6 holds 3 and 1, so its last cell is 2. Across 6 checks out: 4 and 2 make 6.
Which digit goes in the shared cell?
Across 17 and Down 16 each have two cells, and they share the top left cell.
Find the set for each run first. Then look for the digit that is in both.
Try it
Which digit goes in the top left cell?
- 9
- 8
Show the answer
9
Correct. Two cells that add up to 17 must be 8 and 9, and two cells that add up to 16 must be 7 and 9. Only 9 is in both sets, so the top left cell is 9.
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