Strategy
Kakuro Strategy & Tips
A practical strategy guide for Kakuro: memorise the unique sums, start with short and extreme runs, let crossing runs eliminate digits, and keep pencil notes clean.
Play KakuroThe core idea
Narrow first, place second
Almost every strong Kakuro habit comes down to two ideas: know which digit sets a sum allows, and intersect the candidates of the two runs that cross each cell. Guessing is never needed — every puzzle here has exactly one solution — so the skill is spotting which deduction is available right now.
- 01
Memorise the unique sums
Some totals can be built only one way for a given run length: 3 and 4 in two cells, 6 and 7 in three, 10 and 11 in four, and their mirror images at the top end (16 and 17, 23 and 24, 29 and 30). Knowing these on sight lets you fill or heavily restrict a run the moment you read its clue. The table below lists the ones worth learning.
- 02
Start with short, extreme runs
Scan the whole grid before you place a digit. Two-cell runs with a very small or very large total have one or two options; three-cell runs with 6, 7, 23 or 24 have one. Those cells anchor the solve, and their neighbours in the crossing runs shrink quickly.
- 03
Let crossings do the work
Every cell sits in two runs. Write the candidates each run allows, then intersect them: a cell that can be 1, 2 or 4 in its across run and 2, 3 or 5 in its down run can only be 2. Most Kakuro deductions are this single move, repeated.
- 04
Use the remainder
When some cells in a run are known, subtract them from the clue. If a run of four with clue 20 already has 9 and 6, the other two cells must add to 5 using digits other than 9 and 6 — 1+4 or 2+3. Constantly working with the remainder keeps candidate sets honest.
- 05
Watch for one-digit differences
Sometimes a run’s clue allows two digit sets that differ by only one digit, such as 1 2 5 and 1 3 4 for a total of 8 in three cells. The digits common to every option (here 1) are certain; the others are decided by the crossing runs.
- 06
Keep notes clean and current
Pencil marks are a tool, not a record of everything that could conceivably fit. Note only the digits the sums allow, remove a note as soon as a placement kills it, and use the auto-notes button to rebuild candidates after a large deduction.
Cheat sheet
Sums with a single combination
For each run length, these are the totals that can be built only one way. Reading one of them in a clue tells you the run's digits immediately.
2 cells
- 31 2
- 41 3
- 167 9
- 178 9
3 cells
- 61 2 3
- 71 2 4
- 236 8 9
- 247 8 9
4 cells
- 101 2 3 4
- 111 2 3 5
- 295 7 8 9
- 306 7 8 9
5 cells
- 151 2 3 4 5
- 161 2 3 4 6
- 344 6 7 8 9
- 355 6 7 8 9
6 cells
- 211 2 3 4 5 6
- 221 2 3 4 5 7
- 383 5 6 7 8 9
- 394 5 6 7 8 9
By size
How the approach shifts with grid size
The habits above apply to every size. What changes is how long candidates stay open — see the sizes section of the guide.
Easy
Runs are short, so unique sums and two-cell totals do most of the work. Practise reading a clue and reaching for the combination without notes.
Medium
Runs of four and five appear. Start using notes, and check the combination helper for the cell you are stuck on before you place anything.
Hard
Six-cell runs leave many possibilities for a long time. Work the extremes first, keep every note current, and expect the last third of the grid to fall quickly once a few crossings resolve.
Ready to put it into practice? Read the full how-to-play guide or jump straight in.
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