Kakuro for beginners
Kakuro is a crossword with digits. Each run of white squares adds up to the clue beside it, using the digits 1 to 9 with no repeats in a run. You only need addition and a handful of sums worth remembering.
Reading the clues
Clues sit in the black squares, split by a diagonal line. The number above the line is the total for the run of white squares to its right; the number below the line is the total for the run underneath it. Every white square belongs to one across run and one down run.
The sums worth learning
Some totals can only be made one way. These are where every Kakuro starts:
| Squares | Smallest | Largest |
|---|---|---|
| 2 | 3 = 1+2 · 4 = 1+3 | 16 = 7+9 · 17 = 8+9 |
| 3 | 6 = 1+2+3 · 7 = 1+2+4 | 23 = 6+8+9 · 24 = 7+8+9 |
| 4 | 10 = 1+2+3+4 · 11 = 1+2+3+5 | 29 = 5+7+8+9 · 30 = 6+7+8+9 |
The full list for every length is in the Kakuro combinations table.
A first puzzle
Seven white squares, six clues. Try it on paper first if you like.
Solving it, step by step
Find a two-square run with a unique sum
The top across run is 4 in two squares. The only pair of different digits that makes 4 is 1 + 3 (2 + 2 would repeat a digit). So these squares hold 1 and 3, in some order.
Cross it with another unique run
The left down run is 3 in two squares: only 1 + 2. The top-left square belongs to both runs, so it must be in {1, 3} and in {1, 2} — the only digit in both is 1.
Finish both runs
With 1 placed, the across run of 4 needs a 3 beside it, and the down run of 3 needs a 2 below it.
Do the same at the other corner
The bottom across run is 16 in two squares — only 7 + 9. The right down run is 17 in two squares — only 8 + 9. Their shared square must be 9, so the others are 7 and 8.
Use the sum to fill the last square
The middle across run is 19: 2 + ? + 8 = 19, so the middle square is 9. Check it the other way: the middle down run is 3 + 9 + 7 = 19. ✓
What to remember
- Start with unique sums, especially where two of them cross.
- Where runs cross, the digit must suit both. Write the possible digits small and keep only those that fit both runs.
- Finish with arithmetic. When all but one square of a run is known, the last one is just the total minus the rest.
- Check both ways. Every digit is in an across run and a down run — a quick check catches slips early.
Next steps
Play Kakuro on Easy with a small grid, keep the combination calculator open in another tab, and when you are stuck, enter the puzzle in the Kakuro Solver to see the next step explained. Enjoyed it? Killer Sudoku and Calcudoku use the same cage-sum thinking.
Questions
Is Kakuro hard?
It looks it, but a beginner puzzle needs only addition and a few memorised sums. Start with the Easy level and small grids.
Can a digit repeat in Kakuro?
Not within one run. The same digit can appear again in a different run, even in the same row, if a black square separates them.
What is a unique sum?
A total that can be made only one way with different digits — such as 3 in two squares (1 + 2) or 24 in three (7 + 8 + 9). They are the best places to start.
How do I find every combination for a run?
Use the Kakuro combination calculator, or the full Kakuro combinations table.