Kakuro

Kakuro Combinations Chart — Complete Reference

6 min read  ·  Burmly

Every Kakuro clue tells you the sum of a run of cells, each containing a unique digit from 1 to 9. Some clues have only one valid combination of digits — meaning both the values and their placement are forced. Others have many options, requiring cross-referencing with intersecting clues.

This page gives you the complete reference: every valid combination for 2-cell, 3-cell, 4-cell, and 5-cell runs, organized by sum.

Forced combinations — memorize these first

These clue/length combinations have exactly one valid set of digits. Once you see them, the values are determined immediately. Only the arrangement within the run needs figuring out.

SumLengthOnly combinationNote
32 cells{1, 2}Only way to sum 3 with 2 digits
42 cells{1, 3}
162 cells{7, 9}
172 cells{8, 9}Maximum 2-cell sum
63 cells{1, 2, 3}Minimum 3-cell sum
73 cells{1, 2, 4}
233 cells{6, 8, 9}
243 cells{7, 8, 9}Maximum 3-cell sum
104 cells{1, 2, 3, 4}Minimum 4-cell sum
114 cells{1, 2, 3, 5}
294 cells{5, 7, 8, 9}
304 cells{6, 7, 8, 9}Maximum 4-cell sum
155 cells{1, 2, 3, 4, 5}Minimum 5-cell sum
355 cells{5, 6, 7, 8, 9}Maximum 5-cell sum
Strategy: Always start your solve by marking all forced combinations. These cells' digit sets are locked — any intersecting clue must use digits compatible with them.

2-cell combinations — complete list

Each entry shows every valid pair of digits for that sum. All digits must be different (1–9).

SumOptionsValid combinations
31{1,2}
41{1,3}
52{1,4}    {2,3}
62{1,5}    {2,4}
73{1,6}    {2,5}    {3,4}
83{1,7}    {2,6}    {3,5}
94{1,8}    {2,7}    {3,6}    {4,5}
104{1,9}    {2,8}    {3,7}    {4,6}
114{2,9}    {3,8}    {4,7}    {5,6}
123{3,9}    {4,8}    {5,7}
133{4,9}    {5,8}    {6,7}
142{5,9}    {6,8}
152{6,9}    {7,8}
161{7,9}
171{8,9}

3-cell combinations — complete list

SumOptionsValid combinations
61{1,2,3}
71{1,2,4}
82{1,2,5}    {1,3,4}
93{1,2,6}    {1,3,5}    {2,3,4}
104{1,2,7}    {1,3,6}    {1,4,5}    {2,3,5}
115{1,2,8}    {1,3,7}    {1,4,6}    {2,3,6}    {2,4,5}
127{1,2,9}    {1,3,8}    {1,4,7}    {1,5,6}    {2,3,7}    {2,4,6}    {3,4,5}
137{1,3,9}    {1,4,8}    {1,5,7}    {2,3,8}    {2,4,7}    {2,5,6}    {3,4,6}
148{1,4,9}    {1,5,8}    {1,6,7}    {2,3,9}    {2,4,8}    {2,5,7}    {3,4,7}    {3,5,6}
158{1,5,9}    {1,6,8}    {2,4,9}    {2,5,8}    {2,6,7}    {3,4,8}    {3,5,7}    {4,5,6}
168{1,6,9}    {1,7,8}    {2,5,9}    {2,6,8}    {3,4,9}    {3,5,8}    {3,6,7}    {4,5,7}
177{1,7,9}    {2,6,9}    {2,7,8}    {3,5,9}    {3,6,8}    {4,5,8}    {4,6,7}
187{1,8,9}    {2,7,9}    {3,6,9}    {3,7,8}    {4,5,9}    {4,6,8}    {5,6,7}
195{2,8,9}    {3,7,9}    {4,6,9}    {4,7,8}    {5,6,8}
204{3,8,9}    {4,7,9}    {5,6,9}    {5,7,8}
213{4,8,9}    {5,7,9}    {6,7,8}
222{5,8,9}    {6,7,9}
231{6,8,9}
241{7,8,9}

How to use this chart while solving

  1. Find all forced combinations first. Mark them — their digit sets are certain.
  2. Cross-reference intersections. A cell at the intersection of two clues must use a digit that appears in valid combinations for both clues.
  3. Eliminate by intersection. If a 2-cell run summing to 8 shares one cell with a 3-cell run summing to 7 ({1,2,4}), the shared cell must be in both {1,7}, {2,6}, or {3,5} AND in {1,2,4}. Only 1, 2, or 4 appear in combinations for sum 8 — but 1+7=8, 3+5=8 don't help. Check: which digits appear in both sum-8 pairs and sum-7 triples? Only 1, 2, 4 appear in sum-7 triples, and of those, 1+7, 2+6 are valid for sum-8. So the intersection could be 1 (if paired with 7) or 2 (if paired with 6).
  4. Use digit frequency. If all valid combinations for a clue contain a specific digit, that digit must appear in the run — even if its exact cell isn't determined yet.

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