Killer Sudoku Online Free | How to Solve Cage Sums

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What Is Killer Sudoku?

Killer Sudoku combines standard Sudoku rules with an extra constraint: the grid is divided into "cages" (groups of cells outlined with dotted lines), and each cage has a target sum printed in its top-left corner. The cells in each cage must:

1. Add up to the target number
2. Contain no repeated digits

Standard Sudoku rules still apply: digits 1–9 must appear exactly once in each row, column, and 3×3 box.

This extra constraint makes Killer Sudoku harder than standard Sudoku in some ways — but it also gives you more information to work with. Paradoxically, good Killer Sudoku players often find it *easier* than hard regular Sudoku once they learn the key techniques.

The 45 Rule: Your Most Powerful Tool

The sum of digits 1 through 9 equals 45. This is the foundation of Killer Sudoku strategy.

Since every row, column, and box must contain each digit 1–9, every row, column, and box sums to exactly 45.

How to use it: If all but one cage in a row is fully contained within that row, you can calculate the missing cell's value by subtracting the other cage sums from 45.

Example: A row has cages summing to 12, 14, and 11. That's 37. So the remaining cell in that row = 45 − 37 = 8.

This technique works for columns and boxes too. It's called an "outies" calculation when cages extend outside a box.

Cage Combination Tables

Two-cell cages have limited options. Memorize these:

Three-cell cages with unique solutions:

When you see a 3-cage sum in a 2-cell cage, you know immediately it's 1+2. You don't need any other information. Start with these fixed cages.

Step-by-Step Solving Approach

Step 1: Find Fixed Cages

Scan for cages whose sum forces a unique digit combination (see table above). Mark those digits as candidates.

Step 2: Apply the 45 Rule

Look at rows, columns, and boxes. If most cages are contained within a single unit, use the 45 rule to determine the value of any "outie" cell.

Step 3: Use Standard Sudoku Techniques

Once you've placed some digits from cage analysis, use regular Sudoku strategies:

• Singles: Only one digit fits in a cell
• Hidden singles: A digit can only go in one place within a row/column/box
• Pairs: Two cells in a unit that must contain the same two digits, eliminating those from other cells

Step 4: Cage Elimination

As you narrow down candidates, cross-check cage sums. If a cage's sum is 11 and you've already placed a 4 in one cell, the other cell must be 7.

Common Killer Sudoku Mistakes

Forgetting the no-repeat rule within cages: A 4-cell cage summing to 10 could theoretically be 1+2+3+4, but if two of those cells are in the same row, you have a conflict. Always check both the cage rule AND the standard Sudoku constraints.

Ignoring large cages: Beginners focus on small cages with unique solutions and ignore larger ones. But large cages often have very few valid combinations once you account for existing row/column constraints.

Not using the 45 rule on boxes: It's easy to remember to use it on rows and columns. Boxes are just as useful.

Killer vs Regular Sudoku: Key Differences

Regular Sudoku gives you some starting digits. Killer Sudoku gives you none — you start with a blank grid and only the cage sums. That's what makes it a genuinely harder puzzle type.

Related Puzzle Games

If you enjoy Killer Sudoku, these number logic puzzles will click with you:

• Sudoku — The classic. Good warm-up before tackling Killer.
• Futoshiki — Inequality constraints instead of cage sums. Similar logic.
• KenKen — Uses arithmetic operations (add, subtract, multiply, divide) in cages. Very similar to Killer Sudoku.
• Kakuro — Pure cage sums, no box constraints. Often called "crossword sudoku."
• Binairo — Binary logic grid puzzle. Great for lateral thinkers.

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