How to Play Kakuro
What is Kakuro?
Kakuro (also known as Cross Sums or Kakro) is a logic-based number puzzle that combines elements of crossword puzzles and Sudoku. The goal is to fill white cells with digits 1-9 so that each run of cells adds up to its clue, without repeating any digit within a run.
Unlike Sudoku, Kakuro requires both logical deduction and arithmetic skills, making it a favorite among puzzle enthusiasts who enjoy mathematical challenges.
Basic Rules
Understand the Grid
The grid contains three types of cells:
- White cells: Where you enter digits 1-9
- Clue cells: Divided diagonally with one or two numbers
- Black cells: Empty/blocked cells
Reading Clue Cells
Each clue cell has a diagonal line dividing it:
- Top-left number: Sum for the cells directly below
- Bottom-right number: Sum for the cells directly to the right
Fill with Digits 1-9
Enter digits so that each horizontal and vertical "run" (consecutive white cells) adds up to the clue for that run.
No Repeating Digits
Within any single run (horizontal or vertical), each digit can only appear once. However, the same digit can appear in different runs.
Key Combinations to Know
Memorizing these unique combinations will speed up your solving:
2-Cell Runs (Unique)
3 = 1+2
4 = 1+3
16 = 7+9
17 = 8+9
3-Cell Runs (Unique)
6 = 1+2+3
7 = 1+2+4
23 = 6+8+9
24 = 7+8+9
4-Cell Runs (Unique)
10 = 1+2+3+4
11 = 1+2+3+5
29 = 5+7+8+9
30 = 6+7+8+9
Remember
Min sum for n cells: 1+2+...+n
Max sum for n cells: 9+8+...+(10-n)
Sum of 1-9 = 45
Solving Strategies
1. Start with Unique Combinations
Look for clues that have only one possible combination of digits. For example, 17 in 2 cells must be 8+9, and 3 in 2 cells must be 1+2.
2. Use Cross-Referencing
When a cell belongs to both a horizontal and vertical run, use the intersection of possible values from both runs to narrow down options.
3. Pencil Mark Candidates
Write small candidate numbers in cells when you're not sure. This helps visualize possibilities and spot patterns.
4. Eliminate by Exclusion
If a digit is used elsewhere in the same run, cross it off as a candidate for other cells in that run.
5. Look for Forced Digits
If the remaining sum in a partial run can only be achieved by one digit, that digit is forced. For example, if you need 8 with one cell and 9 is already used, 8 must go there.
6. Complete Near-Full Runs
When a run has only one empty cell, calculate the required digit: subtract the filled digits from the target sum.
Example Walkthrough
Consider a 2-cell horizontal run with clue 17 intersecting a 3-cell vertical run with clue 24:
- 17 in 2 cells must be 8+9 (only combination)
- 24 in 3 cells must be 7+8+9 (only combination)
- The intersection cell must contain a digit in both {8,9} AND {7,8,9}, which gives us {8,9}
- Look at the other run's constraints to determine if it's 8 or 9
Pro Tips
- ✓Start with the smallest and largest clues - they have fewer combinations
- ✓Focus on cells where horizontal and vertical runs intersect
- ✓Use pencil marks liberally - they help avoid mistakes
- ✓Remember: 0 is never used, only digits 1-9
- ✓If stuck, look for runs where you've already placed some digits