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Kakuro combinations chart

Every way to make each Kakuro total from different digits, for runs of two to nine cells: 502 sets in all. The 34 magic blocks, totals with only one set, are marked.

How to read the chart

Each entry starts with the clue total. Its sets are drawn on nine columns, one per digit, so the same digit always sits in the same place and gaps stand out. Under each total, always lists digits found in every set (the run must contain them) and never lists digits found in none (no cell of the run can hold them).

Run length

Two cells

36 sets for 15 totals, 3 to 17.

  1. 3 in 2 cells, magic block

    • 1 2

    Only one way

  2. 4 in 2 cells, magic block

    • 1 3

    Only one way

  3. 5 in 2 cells

    • 1 4
    • 2 3

    Never 5 6 7 8 9

  4. 6 in 2 cells

    • 1 5
    • 2 4

    Never 3 6 7 8 9

  5. 7 in 2 cells

    • 1 6
    • 2 5
    • 3 4

    Never 7 8 9

  6. 8 in 2 cells

    • 1 7
    • 2 6
    • 3 5

    Never 4 8 9

  7. 9 in 2 cells

    • 1 8
    • 2 7
    • 3 6
    • 4 5

    Never 9

  8. 10 in 2 cells

    • 1 9
    • 2 8
    • 3 7
    • 4 6

    Never 5

  9. 11 in 2 cells

    • 2 9
    • 3 8
    • 4 7
    • 5 6

    Never 1

  10. 12 in 2 cells

    • 3 9
    • 4 8
    • 5 7

    Never 1 2 6

  11. 13 in 2 cells

    • 4 9
    • 5 8
    • 6 7

    Never 1 2 3

  12. 14 in 2 cells

    • 5 9
    • 6 8

    Never 1 2 3 4 7

  13. 15 in 2 cells

    • 6 9
    • 7 8

    Never 1 2 3 4 5

  14. 16 in 2 cells, magic block

    • 7 9

    Only one way

  15. 17 in 2 cells, magic block

    • 8 9

    Only one way

Three cells

84 sets for 19 totals, 6 to 24.

  1. 6 in 3 cells, magic block

    • 1 2 3

    Only one way

  2. 7 in 3 cells, magic block

    • 1 2 4

    Only one way

  3. 8 in 3 cells

    • 1 2 5
    • 1 3 4

    Always 1; never 6 7 8 9

  4. 9 in 3 cells

    • 1 2 6
    • 1 3 5
    • 2 3 4

    Never 7 8 9

  5. 10 in 3 cells

    • 1 2 7
    • 1 3 6
    • 1 4 5
    • 2 3 5

    Never 8 9

  6. 11 in 3 cells

    • 1 2 8
    • 1 3 7
    • 1 4 6
    • 2 3 6
    • 2 4 5

    Never 9

  7. 12 in 3 cells

    • 1 2 9
    • 1 3 8
    • 1 4 7
    • 1 5 6
    • 2 3 7
    • 2 4 6
    • 3 4 5

    Any digit can appear

  8. 13 in 3 cells

    • 1 3 9
    • 1 4 8
    • 1 5 7
    • 2 3 8
    • 2 4 7
    • 2 5 6
    • 3 4 6

    Any digit can appear

  9. 14 in 3 cells

    • 1 4 9
    • 1 5 8
    • 1 6 7
    • 2 3 9
    • 2 4 8
    • 2 5 7
    • 3 4 7
    • 3 5 6

    Any digit can appear

  10. 15 in 3 cells

    • 1 5 9
    • 1 6 8
    • 2 4 9
    • 2 5 8
    • 2 6 7
    • 3 4 8
    • 3 5 7
    • 4 5 6

    Any digit can appear

  11. 16 in 3 cells

    • 1 6 9
    • 1 7 8
    • 2 5 9
    • 2 6 8
    • 3 4 9
    • 3 5 8
    • 3 6 7
    • 4 5 7

    Any digit can appear

  12. 17 in 3 cells

    • 1 7 9
    • 2 6 9
    • 2 7 8
    • 3 5 9
    • 3 6 8
    • 4 5 8
    • 4 6 7

    Any digit can appear

  13. 18 in 3 cells

    • 1 8 9
    • 2 7 9
    • 3 6 9
    • 3 7 8
    • 4 5 9
    • 4 6 8
    • 5 6 7

    Any digit can appear

  14. 19 in 3 cells

    • 2 8 9
    • 3 7 9
    • 4 6 9
    • 4 7 8
    • 5 6 8

    Never 1

  15. 20 in 3 cells

    • 3 8 9
    • 4 7 9
    • 5 6 9
    • 5 7 8

    Never 1 2

  16. 21 in 3 cells

    • 4 8 9
    • 5 7 9
    • 6 7 8

    Never 1 2 3

  17. 22 in 3 cells

    • 5 8 9
    • 6 7 9

    Always 9; never 1 2 3 4

  18. 23 in 3 cells, magic block

    • 6 8 9

    Only one way

  19. 24 in 3 cells, magic block

    • 7 8 9

    Only one way

Four cells

126 sets for 21 totals, 10 to 30.

  1. 10 in 4 cells, magic block

    • 1 2 3 4

    Only one way

  2. 11 in 4 cells, magic block

    • 1 2 3 5

    Only one way

  3. 12 in 4 cells

    • 1 2 3 6
    • 1 2 4 5

    Always 1 2; never 7 8 9

  4. 13 in 4 cells

    • 1 2 3 7
    • 1 2 4 6
    • 1 3 4 5

    Always 1; never 8 9

  5. 14 in 4 cells

    • 1 2 3 8
    • 1 2 4 7
    • 1 2 5 6
    • 1 3 4 6
    • 2 3 4 5

    Never 9

  6. 15 in 4 cells

    • 1 2 3 9
    • 1 2 4 8
    • 1 2 5 7
    • 1 3 4 7
    • 1 3 5 6
    • 2 3 4 6

    Any digit can appear

  7. 16 in 4 cells

    • 1 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 6

    Any digit can appear

  8. 17 in 4 cells

    • 1 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 6

    Any digit can appear

  9. 18 in 4 cells

    • 1 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 6

    Any digit can appear

  10. 19 in 4 cells

    • 1 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 7

    Any digit can appear

  11. 20 in 4 cells

    • 1 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 7

    Any digit can appear

  12. 21 in 4 cells

    • 1 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 7

    Any digit can appear

  13. 22 in 4 cells

    • 1 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 7

    Any digit can appear

  14. 23 in 4 cells

    • 1 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 8

    Any digit can appear

  15. 24 in 4 cells

    • 1 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 8

    Any digit can appear

  16. 25 in 4 cells

    • 1 7 8 9
    • 2 6 8 9
    • 3 5 8 9
    • 3 6 7 9
    • 4 5 7 9
    • 4 6 7 8

    Any digit can appear

  17. 26 in 4 cells

    • 2 7 8 9
    • 3 6 8 9
    • 4 5 8 9
    • 4 6 7 9
    • 5 6 7 8

    Never 1

  18. 27 in 4 cells

    • 3 7 8 9
    • 4 6 8 9
    • 5 6 7 9

    Always 9; never 1 2

  19. 28 in 4 cells

    • 4 7 8 9
    • 5 6 8 9

    Always 8 9; never 1 2 3

  20. 29 in 4 cells, magic block

    • 5 7 8 9

    Only one way

  21. 30 in 4 cells, magic block

    • 6 7 8 9

    Only one way

Five cells

126 sets for 21 totals, 15 to 35.

  1. 15 in 5 cells, magic block

    • 1 2 3 4 5

    Only one way

  2. 16 in 5 cells, magic block

    • 1 2 3 4 6

    Only one way

  3. 17 in 5 cells

    • 1 2 3 4 7
    • 1 2 3 5 6

    Always 1 2 3; never 8 9

  4. 18 in 5 cells

    • 1 2 3 4 8
    • 1 2 3 5 7
    • 1 2 4 5 6

    Always 1 2; never 9

  5. 19 in 5 cells

    • 1 2 3 4 9
    • 1 2 3 5 8
    • 1 2 3 6 7
    • 1 2 4 5 7
    • 1 3 4 5 6

    Always 1

  6. 20 in 5 cells

    • 1 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 6

    Any digit can appear

  7. 21 in 5 cells

    • 1 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 7

    Any digit can appear

  8. 22 in 5 cells

    • 1 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 7

    Any digit can appear

  9. 23 in 5 cells

    • 1 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 7

    Any digit can appear

  10. 24 in 5 cells

    • 1 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 7

    Any digit can appear

  11. 25 in 5 cells

    • 1 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 7

    Any digit can appear

  12. 26 in 5 cells

    • 1 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 8

    Any digit can appear

  13. 27 in 5 cells

    • 1 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 8

    Any digit can appear

  14. 28 in 5 cells

    • 1 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 8

    Any digit can appear

  15. 29 in 5 cells

    • 1 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 8

    Any digit can appear

  16. 30 in 5 cells

    • 1 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 8

    Any digit can appear

  17. 31 in 5 cells

    • 1 6 7 8 9
    • 2 5 7 8 9
    • 3 4 7 8 9
    • 3 5 6 8 9
    • 4 5 6 7 9

    Always 9

  18. 32 in 5 cells

    • 2 6 7 8 9
    • 3 5 7 8 9
    • 4 5 6 8 9

    Always 8 9; never 1

  19. 33 in 5 cells

    • 3 6 7 8 9
    • 4 5 7 8 9

    Always 7 8 9; never 1 2

  20. 34 in 5 cells, magic block

    • 4 6 7 8 9

    Only one way

  21. 35 in 5 cells, magic block

    • 5 6 7 8 9

    Only one way

Six cells

84 sets for 19 totals, 21 to 39.

  1. 21 in 6 cells, magic block

    • 1 2 3 4 5 6

    Only one way

  2. 22 in 6 cells, magic block

    • 1 2 3 4 5 7

    Only one way

  3. 23 in 6 cells

    • 1 2 3 4 5 8
    • 1 2 3 4 6 7

    Always 1 2 3 4; never 9

  4. 24 in 6 cells

    • 1 2 3 4 5 9
    • 1 2 3 4 6 8
    • 1 2 3 5 6 7

    Always 1 2 3

  5. 25 in 6 cells

    • 1 2 3 4 6 9
    • 1 2 3 4 7 8
    • 1 2 3 5 6 8
    • 1 2 4 5 6 7

    Always 1 2

  6. 26 in 6 cells

    • 1 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 7

    Always 1

  7. 27 in 6 cells

    • 1 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 7

    Any digit can appear

  8. 28 in 6 cells

    • 1 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 8

    Any digit can appear

  9. 29 in 6 cells

    • 1 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 8

    Any digit can appear

  10. 30 in 6 cells

    • 1 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 8

    Any digit can appear

  11. 31 in 6 cells

    • 1 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 8

    Any digit can appear

  12. 32 in 6 cells

    • 1 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 8

    Any digit can appear

  13. 33 in 6 cells

    • 1 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 8

    Any digit can appear

  14. 34 in 6 cells

    • 1 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 9

    Always 9

  15. 35 in 6 cells

    • 1 4 6 7 8 9
    • 2 3 6 7 8 9
    • 2 4 5 7 8 9
    • 3 4 5 6 8 9

    Always 8 9

  16. 36 in 6 cells

    • 1 5 6 7 8 9
    • 2 4 6 7 8 9
    • 3 4 5 7 8 9

    Always 7 8 9

  17. 37 in 6 cells

    • 2 5 6 7 8 9
    • 3 4 6 7 8 9

    Always 6 7 8 9; never 1

  18. 38 in 6 cells, magic block

    • 3 5 6 7 8 9

    Only one way

  19. 39 in 6 cells, magic block

    • 4 5 6 7 8 9

    Only one way

Seven cells

36 sets for 15 totals, 28 to 42.

  1. 28 in 7 cells, magic block

    • 1 2 3 4 5 6 7

    Only one way

  2. 29 in 7 cells, magic block

    • 1 2 3 4 5 6 8

    Only one way

  3. 30 in 7 cells

    • 1 2 3 4 5 6 9
    • 1 2 3 4 5 7 8

    Always 1 2 3 4 5

  4. 31 in 7 cells

    • 1 2 3 4 5 7 9
    • 1 2 3 4 6 7 8

    Always 1 2 3 4 7

  5. 32 in 7 cells

    • 1 2 3 4 5 8 9
    • 1 2 3 4 6 7 9
    • 1 2 3 5 6 7 8

    Always 1 2 3

  6. 33 in 7 cells

    • 1 2 3 4 6 8 9
    • 1 2 3 5 6 7 9
    • 1 2 4 5 6 7 8

    Always 1 2 6

  7. 34 in 7 cells

    • 1 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 8

    Always 1

  8. 35 in 7 cells

    • 1 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 8

    Always 5

  9. 36 in 7 cells

    • 1 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 9

    Always 9

  10. 37 in 7 cells

    • 1 2 4 6 7 8 9
    • 1 3 4 5 7 8 9
    • 2 3 4 5 6 8 9

    Always 4 8 9

  11. 38 in 7 cells

    • 1 2 5 6 7 8 9
    • 1 3 4 6 7 8 9
    • 2 3 4 5 7 8 9

    Always 7 8 9

  12. 39 in 7 cells

    • 1 3 5 6 7 8 9
    • 2 3 4 6 7 8 9

    Always 3 6 7 8 9

  13. 40 in 7 cells

    • 1 4 5 6 7 8 9
    • 2 3 5 6 7 8 9

    Always 5 6 7 8 9

  14. 41 in 7 cells, magic block

    • 2 4 5 6 7 8 9

    Only one way

  15. 42 in 7 cells, magic block

    • 3 4 5 6 7 8 9

    Only one way

Eight cells

9 sets for 9 totals, 36 to 44.

  1. 36 in 8 cells, magic block

    • 1 2 3 4 5 6 7 8

    All but 9

  2. 37 in 8 cells, magic block

    • 1 2 3 4 5 6 7 9

    All but 8

  3. 38 in 8 cells, magic block

    • 1 2 3 4 5 6 8 9

    All but 7

  4. 39 in 8 cells, magic block

    • 1 2 3 4 5 7 8 9

    All but 6

  5. 40 in 8 cells, magic block

    • 1 2 3 4 6 7 8 9

    All but 5

  6. 41 in 8 cells, magic block

    • 1 2 3 5 6 7 8 9

    All but 4

  7. 42 in 8 cells, magic block

    • 1 2 4 5 6 7 8 9

    All but 3

  8. 43 in 8 cells, magic block

    • 1 3 4 5 6 7 8 9

    All but 2

  9. 44 in 8 cells, magic block

    • 2 3 4 5 6 7 8 9

    All but 1

Nine cells

One set, total 45.

  1. 45 in 9 cells, magic block

    • 1 2 3 4 5 6 7 8 9

    Every digit once