How to Play Kakuro
Kakuro is a logic puzzle that blends a crossword-style grid with arithmetic. You fill white cells with digits so that every row and column run hits an exact sum — no arithmetic shortcuts and no guessing required. This guide walks you from zero to solving your first puzzle.
What you need
Nothing but a browser. Every puzzle on this site generates entirely in-page — no download, no account, no ads interrupting play. The same rules apply to paper Kakuro puzzles, so this guide works for both.
Reading the Kakuro grid
A Kakuro grid has two types of cells:
Clue cells (shaded)
Divided diagonally. The bottom-left number is the target sum for the across run stretching to the right. The top-right number is the target for the down run below. A cell with only one number borders a run in only one direction.
White cells (empty)
These are where you place digits. Each white cell belongs to exactly one across run and one down run (the clue for each is in the nearest shaded cell in that direction). A run is an unbroken horizontal or vertical sequence of white cells.
Example 3×3 grid (numbers are clues, ? cells are yours to fill)
11↓ | 7↓ | |
15→ | ? | ? |
3→ | ? | ? |
→ = across clue, ↓ = down clue. The across run in row 1 must sum to 15; row 2 must sum to 3. The down run in column A must sum to 11; column B must sum to 7.
The three rules
- 1
Fill every white cell with a digit from 1 to 9.
Zero is not a valid digit. Every white cell must contain exactly one of 1–9.
- 2
Each run must sum exactly to its clue value.
The digits in every horizontal and vertical run must add up to the clue shown in the bordering shaded cell. No more, no less.
- 3
No digit may repeat within a single run.
Each of the digits you place within one across run must be unique. Same for each down run. A digit can appear in multiple different runs — just not twice within the same one.
Worked example — step by step
Using the 3×3 grid from above (across clues: 15, 3; down clues: 11, 7):
Step 1 — Find the forced run
Row 2 has a 2-cell across clue of 3. The only pair of distinct digits from 1–9 that sums to 3 is {1, 2}. So those two cells must hold 1 and 2 (order unknown so far). This is a forced combination — start here.
Step 2 — Use the down clue to place 1 and 2
Column B's down clue is 7. Column B has 2 cells: one in row 1, one in row 2. Row 2 column B must be 1 or 2. If it were 2, column B's top cell would need to be 5 (so 5+2=7). If it were 1, column B's top cell would need to be 6 (6+1=7). Both are valid so far — move to column A.
Step 3 — Resolve with the remaining down clue
Column A's down clue is 11. Row 1 has across clue 15, so row 1 cells must sum to 15. Row 1, col A + row 1, col B = 15. Combined with col A down = 11 and col B down = 7: row 1 col A must be 8 and row 1 col B must be 7 (8+7=15, 8+row2A=11 → row 2 col A=3... wait, col A down = row1A + row2A = 11, row2A must be 1 or 2). If row2A=2, then row1A=9; if row1A=9, then row1B=15-9=6; check col B: 6+row2B=7 → row2B=1. And row2A=2, row2B=1 sums to 3. ✓ If row2A=1, then row1A=10 — impossible (max digit is 9). So row2A=2, row2B=1.
Step 4 — Fill in the solution
Row 1: col A = 9, col B = 6. Row 2: col A = 2, col B = 1. Check: across 15 → 9+6=15 ✓, across 3 → 2+1=3 ✓, down col A 11 → 9+2=11 ✓, down col B 7 → 6+1=7 ✓. No repeats within any run ✓. Puzzle solved.
Five tips for beginners
- 1. Start with forced combinations. Short runs at their minimum or maximum sum have only one valid digit set. A 3-in-2 can only be {1,2}; a 17-in-2 can only be {8,9}. Lock these in first.
- 2. Use candidate marks freely. When a cell could hold 2 or 3 values, write them all. The app's Candidates button does this automatically — use it before placing uncertain digits.
- 3. Cross-check every intersection. Each white cell sits at the crossing of an across run and a down run. A digit allowed by across but forbidden by down (or vice versa) can be eliminated immediately.
- 4. Re-scan after each placement. Placing one digit often forces another. After every entry, revisit neighbouring runs — you may find a new forced combination you couldn't see before.
- 5. Never guess. A well-formed Kakuro puzzle has exactly one solution reachable by pure logic. If you feel stuck, look for a crossing constraint you haven't applied yet rather than trying digits at random.
Common beginner mistakes
- ✗ Repeating a digit in a run. 5+5=10 violates rule 3. Every digit in a run must be distinct.
- ✗ Confusing across and down clues. Double-check which triangle is which — the bottom-left number belongs to the across run, not the down run.
- ✗ Placing without checking both crossing runs. A digit valid for one direction may be illegal in the other. Always verify against both the across and down run before placing.
- ✗ Forgetting to update candidates. After each placement, remove that digit from the candidates of every other cell in the same run. Stale candidates lead to wrong placements.
Kakuro vs. Sudoku — what's different?
| Feature | Kakuro | Sudoku |
|---|---|---|
| Grid shape | Irregular runs, like a crossword | Fixed 9×9 with 3×3 boxes |
| Arithmetic | Yes — digits must sum to clues | No — just placement uniqueness |
| Repetition rule | No repeat within any run | No repeat in row, column, or box |
| Key skill | Combination analysis + crossing sums | Pattern recognition + elimination |
Ready to solve?
The best way to learn is to play. Start on Easy — the generator picks a grid solvable with just forced combinations and basic crossing constraints. Use the Hint button if you get stuck; it highlights the most useful cell and explains the deduction.