How to Play Killer Sudoku
Killer Sudoku (also known as Sum Sudoku or Samunamupure) combines classic Sudoku with arithmetic. No given digits—just cages with target sums. This guide teaches you everything you need to know.
What is Killer Sudoku?
Killer Sudoku is a variant of classic Sudoku where the grid starts empty—no given digits. Instead, the grid is divided into cages: outlined groups of cells with a small number in the corner indicating their target sum.
Your goal is to fill the grid with digits 1-9 such that:
Each row contains digits 1-9 exactly once
Each column contains digits 1-9 exactly once
Each 3×3 box contains digits 1-9 exactly once
Digits in each cage sum to the cage's target
All digits within a cage are different from each other
The arithmetic adds a new dimension: you're simultaneously solving a Sudoku puzzle and a set of addition constraints.
Understanding Cages
Cages are the defining feature of Killer Sudoku. Each cage is a contiguous group of cells (usually 2-5 cells, occasionally more) outlined with a dashed border. In the top-left corner of each cage, you'll see a small number—the cage's target sum.
Key Rules for Cages:
1.
Sum constraint. The digits in the cage must add up to exactly the target sum.
2.
No repeats in cage. All digits within a single cage must be different. A 3-cell cage cannot contain two 5s.
3.
Sudoku rules still apply. Cages don't override Sudoku constraints. If two cells in a cage are in the same row, they still must be different (which is already guaranteed by the no-repeat rule).
Example: A 2-cell cage with target sum 5:
Possible combinations: {1,4} or {2,3}
Not allowed: {2,2} (digits must be different) or {0,5} (only 1-9 allowed)
Worked Example: Small Killer Sudoku
Let's solve a simplified 4×4 Killer Sudoku to see the logic in action. (Real puzzles are 9×9, but this demonstrates the principles.)
Starting grid (4×4, digits 1-4):
Four 2-cell cages. Each row/column must contain 1,2,3,4 exactly once.
Step 1: Analyze Cage Combinations
Top-left cage (sum 7, 2 cells): Only {3,4} works (1+2=3, 1+3=4, 1+4=5, 2+3=5, 2+4=6, 3+4=7).
Top-right cage (sum 3, 2 cells): Only {1,2} works.
Bottom-left cage (sum 6, 2 cells): Only {2,4} works.
Bottom-right cage (sum 4, 2 cells): Could be {1,3}.
Step 2: Use Row/Column Constraints
Row 1 must contain 1,2,3,4. Top-left has {3,4}, top-right has {1,2}. All four digits are accounted for!
Row 2 must contain 1,2,3,4. Bottom-left has {2,4}, bottom-right must have {1,3}.
Step 3: Determine Exact Positions
Column 1: Must have 1,2,3,4. Top-left contributes one of{3,4}, bottom-left contributes one of {2,4}. If top-left uses 4, bottom-left cannot use 4 (no repeat in column). So top-left must be 3 (top cell) or 4 (bottom cell of that cage), and bottom-left must be 2 (top cell) or 4 (bottom cell).
By systematically eliminating impossibilities using Sudoku rules + cage sums, we deduce the unique solution.
The key lesson: cage combinations constrain possibilities, and Sudoku rules (rows, columns, boxes) eliminate the rest. Progress comes from combining both types of logic.
Essential Solving Techniques
Full-size Killer Sudoku puzzles require specific techniques. Here are the core methods:
1. Cage Combinations (Level 0)
Identify cages where only one set of digits is possible. Many common cage sizes and sums have unique solutions. This is your primary entry point into any puzzle.
Learn this technique →2. The 45 Rule (Level 1)
Every row, column, and 3×3 box sums to 45 (since 1+2+...+9 = 45). When cages partially overlap a region, you can deduce "innie" or "outie" cells using this fact.
Learn this technique →3. Cage Eliminations (Level 2)
Use the no-repeat-in-cage rule to eliminate candidates. If a cage already has a 5 placed, no other cell in that cage can be 5. Combine with Sudoku rules for powerful deductions.
Learn this technique →4. Advanced Cage Logic (Level 3)
Analyze how cages interact across rows, columns, and boxes. When simpler techniques stall, cross-sum analysis and constraint propagation unlock progress.
Learn this technique →Tips for Success
•
Start with unique combinations
Scan for 2-cell cages with extreme sums (3, 4, 16, 17) and small 3-cell cages (6, 7, 23, 24). These have forced digit sets.
•
Use pencil marks (candidates)
Mark possible digits for each cell. As you eliminate options, the remaining candidates become clear.
•
Look for single-cell cages
Occasionally a cage contains only one cell. That cell's value equals the cage sum—instant progress!
•
Check arithmetic carefully
A single arithmetic mistake early on can cascade into unsolvable conflicts later. Verify sums as you go.
Frequently Asked Questions
Can I guess in Killer Sudoku?
No guessing is needed. Every well-formed Killer Sudoku has exactly one solution reachable through logic combining Sudoku rules and cage arithmetic. The puzzle generator proves uniqueness, though not all puzzles are solvable by pure logic techniques alone.
What does 'no repeat in cage' mean?
All digits within a single cage must be different from each other. For example, a 3-cell cage cannot contain 1, 1, 5 (two 1s). This is in addition to the standard Sudoku uniqueness rules for rows, columns, and boxes.
What's the best technique for beginners?
Start with cage combinations. Look for cages with unique digit sets—like 2-cell cages summing to 3 (must be {1,2}) or 17 (must be {8,9}). These give you immediate constraints without complex reasoning.
How do I know if I made a mistake?
If a cage's sum becomes impossible to satisfy, or if a row/column/box cannot fit all nine digits, you made an error earlier. Use undo to backtrack and reconsider.
Continue Your Killer Sudoku Journey
Cage Combinations
Learn which digit sets are forced for common cage sizes and sums.
The 45 Rule
Master the innies/outies technique using the fact that rows, columns, and boxes sum to 45.
Daily Killer Sudoku Puzzle
Put your skills to the test with today's daily challenge.
Practice Puzzles
Solve unlimited practice puzzles at various difficulty levels.