Killer Sudoku: A Friendly Walkthrough
Killer sudoku looks intimidating because of the cage sums. It's actually friendlier than hard classic, once you know the bag of tricks. Here are the essentials.
Killer sudoku looks intimidating. The grid is broken into dotted-line regions called cages, each with a tiny number in the corner, and the instructions tell you the cages have to sum to those numbers. It feels like a sudoku with an extra crossword glued on.
It is much friendlier than it looks. Killer is still a logic puzzle. The sums are just another constraint, no harder to use than rows and columns, and once you learn the small bag of tricks for handling them, killer puzzles are arguably easier than the hard classics.
The cage cheat sheet
Every cage is small. The smallest cages have two cells, the largest you will see often have four or five. Each cage size has a short list of digit combinations that sum to common targets. Once you know the list, killer becomes much faster.
- Cage sum 3, two cells
- Only 1+2. The cells must hold 1 and 2.
- Cage sum 4, two cells
- Only 1+3.
- Cage sum 16, two cells
- Only 7+9.
- Cage sum 17, two cells
- Only 8+9.
- Cage sum 6, three cells
- Only 1+2+3.
- Cage sum 7, three cells
- Only 1+2+4.
- Cage sum 23, three cells
- Only 6+8+9.
- Cage sum 24, three cells
- Only 7+8+9.
These are the locked combinations. A two-cell cage summing to 3 must be {1, 2}. There is no other option. Spot one of these on the grid and you have effectively been handed two clues for free.
The forty-five rule
Every row, column and box contains the digits 1 through 9, which sum to 45. That fact is the most powerful tool in killer.
Pick a row. Add up the cage sums for all the cages that sit entirely within that row. If a single cage spills into an adjacent row by exactly one cell, you know that intruding cell plus the row sum must equal 45. Subtract, and you have placed a digit. Repeat for columns, repeat for boxes. The rule is unglamorous but it cracks more killer puzzles than anything else.
A worked example
Imagine the top-left box of a killer grid. Three cages live inside it completely. They sum to 12, 18 and 8 respectively, totalling 38. The box must total 45. The remaining cells in the box, which belong to cages that cross over, must therefore contribute 7. If only one cell spills in, that cell is 7. Done.
How killer differs from classic
Killer feels different in two ways. First, you finish more puzzles by arithmetic than by pattern recognition. The sums do half the work. Second, killer grids often have very few given digits, sometimes none, which scares newcomers off before they realise the cages replace the givens.
Once you trust the cages, killer flows as smoothly as a classic medium sudoku. The trick is to lean on the cage logic first, sudoku logic second. Most of the difficulty melts when you do.
When to fall back on classic techniques
Eventually the cage logic stops generating placements and the puzzle becomes a regular sudoku again. That is your cue to fire up naked singles, hidden singles, and if needed, pointing pairs. The same techniques, in the same order.
Killer is one of the most rewarding variants because it asks a different question on every move. You are not just placing digits; you are spending and saving sums. For more on what makes each variant feel different, see the killer sudoku variant page or browse the full variants catalogue.
Keep reading
- A Pencil-Mark Workflow That Actually WorksHalf-marked sudoku grids lie to you. The four-step pencil-mark workflow that keeps medium and hard puzzles honest, plus the cardinal sin to avoid.
- Sudoku Rules Explained in Five MinutesThree rules, one grid, no maths. A quick, complete guide to the rules of sudoku with examples of what counts as valid and what does not.
- What is Sudoku? A Plain-English Guide for BeginnersSudoku is not a maths puzzle. It is a logic puzzle that uses digits as labels. Here is what it actually is, in plain English, and why it caught on.