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Kakuro combinations chart

Calculated exactly for every run length from 2 to 9 squares

Find the number of squares in a run, then its total, to see every set of different digits that can make it. Totals with only one possible set are highlighted, and those are the best places to start a puzzle.

How to read it: each set lists digits, not their order. "1 3" for a two-square run of 4 means the squares are 1 and 3, in an order the crossing runs will decide.

Jump to: 2 squares · 3 squares · 4 squares · 5 squares · 6 squares · 7 squares · 8 squares · 9 squares

2-square runs (totals 3 to 17)

TotalPossible digit setsSets
31 21
41 31
51 4; 2 32
61 5; 2 42
71 6; 2 5; 3 43
81 7; 2 6; 3 53
91 8; 2 7; 3 6; 4 54
101 9; 2 8; 3 7; 4 64
112 9; 3 8; 4 7; 5 64
123 9; 4 8; 5 73
134 9; 5 8; 6 73
145 9; 6 82
156 9; 7 82
167 91
178 91

3-square runs (totals 6 to 24)

TotalPossible digit setsSets
61 2 31
71 2 41
81 2 5; 1 3 42
91 2 6; 1 3 5; 2 3 43
101 2 7; 1 3 6; 1 4 5; 2 3 54
111 2 8; 1 3 7; 1 4 6; 2 3 6; 2 4 55
121 2 9; 1 3 8; 1 4 7; 1 5 6; 2 3 7; 2 4 6; 3 4 57
131 3 9; 1 4 8; 1 5 7; 2 3 8; 2 4 7; 2 5 6; 3 4 67
141 4 9; 1 5 8; 1 6 7; 2 3 9; 2 4 8; 2 5 7; 3 4 7; 3 5 68
151 5 9; 1 6 8; 2 4 9; 2 5 8; 2 6 7; 3 4 8; 3 5 7; 4 5 68
161 6 9; 1 7 8; 2 5 9; 2 6 8; 3 4 9; 3 5 8; 3 6 7; 4 5 78
171 7 9; 2 6 9; 2 7 8; 3 5 9; 3 6 8; 4 5 8; 4 6 77
181 8 9; 2 7 9; 3 6 9; 3 7 8; 4 5 9; 4 6 8; 5 6 77
192 8 9; 3 7 9; 4 6 9; 4 7 8; 5 6 85
203 8 9; 4 7 9; 5 6 9; 5 7 84
214 8 9; 5 7 9; 6 7 83
225 8 9; 6 7 92
236 8 91
247 8 91

4-square runs (totals 10 to 30)

TotalPossible digit setsSets
101 2 3 41
111 2 3 51
121 2 3 6; 1 2 4 52
131 2 3 7; 1 2 4 6; 1 3 4 53
141 2 3 8; 1 2 4 7; 1 2 5 6; 1 3 4 6; 2 3 4 55
151 2 3 9; 1 2 4 8; 1 2 5 7; 1 3 4 7; 1 3 5 6; 2 3 4 66
161 2 4 9; 1 2 5 8; 1 2 6 7; 1 3 4 8; 1 3 5 7; 1 4 5 6; 2 3 4 7; 2 3 5 68
171 2 5 9; 1 2 6 8; 1 3 4 9; 1 3 5 8; 1 3 6 7; 1 4 5 7; 2 3 4 8; 2 3 5 7; 2 4 5 69
181 2 6 9; 1 2 7 8; 1 3 5 9; 1 3 6 8; 1 4 5 8; 1 4 6 7; 2 3 4 9; 2 3 5 8; 2 3 6 7; 2 4 5 7; 3 4 5 611
191 2 7 9; 1 3 6 9; 1 3 7 8; 1 4 5 9; 1 4 6 8; 1 5 6 7; 2 3 5 9; 2 3 6 8; 2 4 5 8; 2 4 6 7; 3 4 5 711
201 2 8 9; 1 3 7 9; 1 4 6 9; 1 4 7 8; 1 5 6 8; 2 3 6 9; 2 3 7 8; 2 4 5 9; 2 4 6 8; 2 5 6 7; 3 4 5 8; 3 4 6 712
211 3 8 9; 1 4 7 9; 1 5 6 9; 1 5 7 8; 2 3 7 9; 2 4 6 9; 2 4 7 8; 2 5 6 8; 3 4 5 9; 3 4 6 8; 3 5 6 711
221 4 8 9; 1 5 7 9; 1 6 7 8; 2 3 8 9; 2 4 7 9; 2 5 6 9; 2 5 7 8; 3 4 6 9; 3 4 7 8; 3 5 6 8; 4 5 6 711
231 5 8 9; 1 6 7 9; 2 4 8 9; 2 5 7 9; 2 6 7 8; 3 4 7 9; 3 5 6 9; 3 5 7 8; 4 5 6 89
241 6 8 9; 2 5 8 9; 2 6 7 9; 3 4 8 9; 3 5 7 9; 3 6 7 8; 4 5 6 9; 4 5 7 88
251 7 8 9; 2 6 8 9; 3 5 8 9; 3 6 7 9; 4 5 7 9; 4 6 7 86
262 7 8 9; 3 6 8 9; 4 5 8 9; 4 6 7 9; 5 6 7 85
273 7 8 9; 4 6 8 9; 5 6 7 93
284 7 8 9; 5 6 8 92
295 7 8 91
306 7 8 91

5-square runs (totals 15 to 35)

TotalPossible digit setsSets
151 2 3 4 51
161 2 3 4 61
171 2 3 4 7; 1 2 3 5 62
181 2 3 4 8; 1 2 3 5 7; 1 2 4 5 63
191 2 3 4 9; 1 2 3 5 8; 1 2 3 6 7; 1 2 4 5 7; 1 3 4 5 65
201 2 3 5 9; 1 2 3 6 8; 1 2 4 5 8; 1 2 4 6 7; 1 3 4 5 7; 2 3 4 5 66
211 2 3 6 9; 1 2 3 7 8; 1 2 4 5 9; 1 2 4 6 8; 1 2 5 6 7; 1 3 4 5 8; 1 3 4 6 7; 2 3 4 5 78
221 2 3 7 9; 1 2 4 6 9; 1 2 4 7 8; 1 2 5 6 8; 1 3 4 5 9; 1 3 4 6 8; 1 3 5 6 7; 2 3 4 5 8; 2 3 4 6 79
231 2 3 8 9; 1 2 4 7 9; 1 2 5 6 9; 1 2 5 7 8; 1 3 4 6 9; 1 3 4 7 8; 1 3 5 6 8; 1 4 5 6 7; 2 3 4 5 9; 2 3 4 6 8; 2 3 5 6 711
241 2 4 8 9; 1 2 5 7 9; 1 2 6 7 8; 1 3 4 7 9; 1 3 5 6 9; 1 3 5 7 8; 1 4 5 6 8; 2 3 4 6 9; 2 3 4 7 8; 2 3 5 6 8; 2 4 5 6 711
251 2 5 8 9; 1 2 6 7 9; 1 3 4 8 9; 1 3 5 7 9; 1 3 6 7 8; 1 4 5 6 9; 1 4 5 7 8; 2 3 4 7 9; 2 3 5 6 9; 2 3 5 7 8; 2 4 5 6 8; 3 4 5 6 712
261 2 6 8 9; 1 3 5 8 9; 1 3 6 7 9; 1 4 5 7 9; 1 4 6 7 8; 2 3 4 8 9; 2 3 5 7 9; 2 3 6 7 8; 2 4 5 6 9; 2 4 5 7 8; 3 4 5 6 811
271 2 7 8 9; 1 3 6 8 9; 1 4 5 8 9; 1 4 6 7 9; 1 5 6 7 8; 2 3 5 8 9; 2 3 6 7 9; 2 4 5 7 9; 2 4 6 7 8; 3 4 5 6 9; 3 4 5 7 811
281 3 7 8 9; 1 4 6 8 9; 1 5 6 7 9; 2 3 6 8 9; 2 4 5 8 9; 2 4 6 7 9; 2 5 6 7 8; 3 4 5 7 9; 3 4 6 7 89
291 4 7 8 9; 1 5 6 8 9; 2 3 7 8 9; 2 4 6 8 9; 2 5 6 7 9; 3 4 5 8 9; 3 4 6 7 9; 3 5 6 7 88
301 5 7 8 9; 2 4 7 8 9; 2 5 6 8 9; 3 4 6 8 9; 3 5 6 7 9; 4 5 6 7 86
311 6 7 8 9; 2 5 7 8 9; 3 4 7 8 9; 3 5 6 8 9; 4 5 6 7 95
322 6 7 8 9; 3 5 7 8 9; 4 5 6 8 93
333 6 7 8 9; 4 5 7 8 92
344 6 7 8 91
355 6 7 8 91

6-square runs (totals 21 to 39)

TotalPossible digit setsSets
211 2 3 4 5 61
221 2 3 4 5 71
231 2 3 4 5 8; 1 2 3 4 6 72
241 2 3 4 5 9; 1 2 3 4 6 8; 1 2 3 5 6 73
251 2 3 4 6 9; 1 2 3 4 7 8; 1 2 3 5 6 8; 1 2 4 5 6 74
261 2 3 4 7 9; 1 2 3 5 6 9; 1 2 3 5 7 8; 1 2 4 5 6 8; 1 3 4 5 6 75
271 2 3 4 8 9; 1 2 3 5 7 9; 1 2 3 6 7 8; 1 2 4 5 6 9; 1 2 4 5 7 8; 1 3 4 5 6 8; 2 3 4 5 6 77
281 2 3 5 8 9; 1 2 3 6 7 9; 1 2 4 5 7 9; 1 2 4 6 7 8; 1 3 4 5 6 9; 1 3 4 5 7 8; 2 3 4 5 6 87
291 2 3 6 8 9; 1 2 4 5 8 9; 1 2 4 6 7 9; 1 2 5 6 7 8; 1 3 4 5 7 9; 1 3 4 6 7 8; 2 3 4 5 6 9; 2 3 4 5 7 88
301 2 3 7 8 9; 1 2 4 6 8 9; 1 2 5 6 7 9; 1 3 4 5 8 9; 1 3 4 6 7 9; 1 3 5 6 7 8; 2 3 4 5 7 9; 2 3 4 6 7 88
311 2 4 7 8 9; 1 2 5 6 8 9; 1 3 4 6 8 9; 1 3 5 6 7 9; 1 4 5 6 7 8; 2 3 4 5 8 9; 2 3 4 6 7 9; 2 3 5 6 7 88
321 2 5 7 8 9; 1 3 4 7 8 9; 1 3 5 6 8 9; 1 4 5 6 7 9; 2 3 4 6 8 9; 2 3 5 6 7 9; 2 4 5 6 7 87
331 2 6 7 8 9; 1 3 5 7 8 9; 1 4 5 6 8 9; 2 3 4 7 8 9; 2 3 5 6 8 9; 2 4 5 6 7 9; 3 4 5 6 7 87
341 3 6 7 8 9; 1 4 5 7 8 9; 2 3 5 7 8 9; 2 4 5 6 8 9; 3 4 5 6 7 95
351 4 6 7 8 9; 2 3 6 7 8 9; 2 4 5 7 8 9; 3 4 5 6 8 94
361 5 6 7 8 9; 2 4 6 7 8 9; 3 4 5 7 8 93
372 5 6 7 8 9; 3 4 6 7 8 92
383 5 6 7 8 91
394 5 6 7 8 91

7-square runs (totals 28 to 42)

TotalPossible digit setsSets
281 2 3 4 5 6 71
291 2 3 4 5 6 81
301 2 3 4 5 6 9; 1 2 3 4 5 7 82
311 2 3 4 5 7 9; 1 2 3 4 6 7 82
321 2 3 4 5 8 9; 1 2 3 4 6 7 9; 1 2 3 5 6 7 83
331 2 3 4 6 8 9; 1 2 3 5 6 7 9; 1 2 4 5 6 7 83
341 2 3 4 7 8 9; 1 2 3 5 6 8 9; 1 2 4 5 6 7 9; 1 3 4 5 6 7 84
351 2 3 5 7 8 9; 1 2 4 5 6 8 9; 1 3 4 5 6 7 9; 2 3 4 5 6 7 84
361 2 3 6 7 8 9; 1 2 4 5 7 8 9; 1 3 4 5 6 8 9; 2 3 4 5 6 7 94
371 2 4 6 7 8 9; 1 3 4 5 7 8 9; 2 3 4 5 6 8 93
381 2 5 6 7 8 9; 1 3 4 6 7 8 9; 2 3 4 5 7 8 93
391 3 5 6 7 8 9; 2 3 4 6 7 8 92
401 4 5 6 7 8 9; 2 3 5 6 7 8 92
412 4 5 6 7 8 91
423 4 5 6 7 8 91

8-square runs (totals 36 to 44)

TotalPossible digit setsSets
361 2 3 4 5 6 7 81
371 2 3 4 5 6 7 91
381 2 3 4 5 6 8 91
391 2 3 4 5 7 8 91
401 2 3 4 6 7 8 91
411 2 3 5 6 7 8 91
421 2 4 5 6 7 8 91
431 3 4 5 6 7 8 91
442 3 4 5 6 7 8 91

9-square runs (totals 45 to 45)

TotalPossible digit setsSets
451 2 3 4 5 6 7 8 91

Why some totals have only one combination

There are 34 totals in this chart that can be made in only one way. They sit at the two ends of each run length: the smallest totals use the lowest digits, and the largest use the highest. For a nine-square run there's only one total possible, 45, because it must use every digit from 1 to 9.

Once you've placed a few of these forced runs, look at where they cross other runs. A square that's 1 or 2 in one direction and 1 or 3 in the other must be 1. That's the main technique explained in how to play Kakuro.

Stuck on a whole puzzle? Use the Kakuro solver.