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Kakuro Cheat Sheet
Everything you need to solve Kakuro faster: all forced combinations, min/max sum bounds, and a concise strategy guide. Use on screen or print it out.
Forced combinations cheat sheet
A forced combination has exactly one valid digit set for its sum and run length. Memorise these — you can fill them in immediately without any guessing or intersection work. Starred runs (★) are the most common in easy and medium puzzles.
| Cells | Sum | Forced digits |
|---|---|---|
| 2 cells | 3★ | {1, 2} |
| 2 cells | 17★ | {8, 9} |
| 3 cells | 6★ | {1, 2, 3} |
| 3 cells | 7 | {1, 2, 4} |
| 3 cells | 23 | {6, 8, 9} |
| 3 cells | 24★ | {7, 8, 9} |
| 4 cells | 10★ | {1, 2, 3, 4} |
| 4 cells | 11 | {1, 2, 3, 5} |
| 4 cells | 29 | {5, 7, 8, 9} |
| 4 cells | 30★ | {6, 7, 8, 9} |
| 5 cells | 15★ | {1, 2, 3, 4, 5} |
| 5 cells | 16 | {1, 2, 3, 4, 6} |
| 5 cells | 34 | {4, 6, 7, 8, 9} |
| 5 cells | 35★ | {5, 6, 7, 8, 9} |
| 6 cells | 21 | {1, 2, 3, 4, 5, 6} |
| 6 cells | 22 | {1, 2, 3, 4, 5, 7} |
| 6 cells | 38 | {3, 5, 6, 7, 8, 9} |
| 6 cells | 39 | {4, 5, 6, 7, 8, 9} |
| 7 cells | 28 | {1, 2, 3, 4, 5, 6, 7} |
| 7 cells | 29 | {1, 2, 3, 4, 5, 6, 8} |
| 7 cells | 41 | {2, 4, 5, 6, 7, 8, 9} |
| 7 cells | 42 | {3, 4, 5, 6, 7, 8, 9} |
| 8 cells | 36 | {1, 2, 3, 4, 5, 6, 7, 8} |
| 8 cells | 37 | {1, 2, 3, 4, 5, 6, 7, 9} |
| 8 cells | 38 | {1, 2, 3, 4, 5, 6, 8, 9} |
| 8 cells | 39 | {1, 2, 3, 4, 5, 7, 8, 9} |
| 8 cells | 40 | {1, 2, 3, 4, 6, 7, 8, 9} |
| 8 cells | 41 | {1, 2, 3, 5, 6, 7, 8, 9} |
| 8 cells | 42 | {1, 2, 4, 5, 6, 7, 8, 9} |
| 8 cells | 43 | {1, 3, 4, 5, 6, 7, 8, 9} |
| 8 cells | 44 | {2, 3, 4, 5, 6, 7, 8, 9} |
| 9 cells | 45 | {1, 2, 3, 4, 5, 6, 7, 8, 9} |
★ = most common in easy/medium puzzles. Memorise these first. For every combination (not just forced ones), see the full combination reference.
Min & max sums by run length
Use this table to immediately spot extreme-sum runs — they have the fewest valid combinations and are the easiest entry points in any puzzle.
| Cells (n) | Min sum | Min digit set | Max sum | Max digit set |
|---|---|---|---|---|
| 2 | 3 | {1, 2} | 17 | {8, 9} |
| 3 | 6 | {1, 2, 3} | 24 | {7, 8, 9} |
| 4 | 10 | {1, 2, 3, 4} | 30 | {6, 7, 8, 9} |
| 5 | 15 | {1, 2, 3, 4, 5} | 35 | {5, 6, 7, 8, 9} |
| 6 | 21 | {1, 2, 3, 4, 5, 6} | 39 | {4, 5, 6, 7, 8, 9} |
| 7 | 28 | {1, 2, 3, 4, 5, 6, 7} | 42 | {3, 4, 5, 6, 7, 8, 9} |
| 8 | 36 | {1, 2, 3, 4, 5, 6, 7, 8} | 44 | {2, 3, 4, 5, 6, 7, 8, 9} |
| 9 | 45 | {1, 2, 3, 4, 5, 6, 7, 8, 9} | 45 | {1, 2, 3, 4, 5, 6, 7, 8, 9} |
Formula: min = n(n+1)/2 · max = n(19−n)/2. A 9-cell run always sums to 45.
Solving strategy cheat sheet
- 1 Scan for forced combinations. Look up every run in the forced table above. If a run is forced, write in all its digits immediately — you only need to determine placement, not identity.
- 2 Find extreme-sum runs. Runs near their min or max bound have very few valid combinations. Check the bounds table, then look up those specific sums in the combination reference.
- 3 Apply intersection logic. At each white cell, the valid digits are the intersection of what both crossing runs allow. Eliminate candidates that appear in neither. Use the game's candidate mode to track this.
- 4 Use residual sums. Subtract placed digits from the run total. Look up the residual sum in the helper to find which digits the remaining cells must contain.
- 5 Fill single-candidate cells. After intersection and residual work, any cell with exactly one remaining candidate can be placed. Each placement may unblock more cells — keep cycling.
Advanced techniques (naked pairs, X-wing, combination pruning) are covered in the technique library.
Clue notation reference
Across clue (upper-right)
The number in the upper-right triangle of a clue cell is the target sum for the white cells extending to the right. Count white cells to the right until you hit a black cell — that is the run.
Down clue (lower-left)
The number in the lower-left triangle is the target sum for the white cells extending downward. Count white cells going down until you hit a black cell — that is the run.
No-repeat rule
Within a single run, each digit 1–9 may appear at most once. The same digit can appear in the same row or column if it belongs to a different run.
Valid digits
Only digits 1 through 9 are allowed. Zero is not a valid entry. Every white cell must be filled — no cell may be left blank in a completed puzzle.
Kakuro cheat sheet — FAQ
- What are forced combinations in Kakuro?
- A forced combination is a run where only one valid set of distinct digits exists. For example, a 2-cell run summing to 3 can only be 2. These are your starting moves in every puzzle — look for them first.
- How do I use this cheat sheet to solve faster?
- Scan the grid for forced combinations first (use the table above). Then identify extreme-sum runs using the bounds table. Use intersection logic at each cell and the Kakuro helper for on-the-fly lookups.
- Can I print this page?
- Yes — use Ctrl+P / Cmd+P in your browser. The tables are formatted to print cleanly. For a more comprehensive printable reference, see the combination reference.
- What is the minimum sum for a 3-cell run?
- 6. The minimum for any n-cell run is 1+2+…+n = n(n+1)/2. For 3 cells: 1+2+3 = 6. The maximum is 7+8+9 = 24. Any 3-cell run clue must fall between 6 and 24 inclusive.
- How is this different from the Kakuro combination reference?
- This cheat sheet summarises the most useful combinations and strategy in a compact format. The full combination reference lists every valid digit set for every sum and run length — much more comprehensive but longer to browse.
- What is the difference between a cheat sheet and a Kakuro solver?
- A cheat sheet is a reference you use yourself to solve faster. A Kakuro solver computes the answer to a specific puzzle automatically. The cheat sheet builds your skill; the solver just gives you the answer without teaching anything.