Killer Sudoku Cheat Sheet: Cage Combinations and the 45 Rule

A Killer Sudoku cheat sheet is a reference of every valid digit combination for each cage size and sum. Because no digit may repeat inside a cage, the number of possible combinations is finite — 502 in total for a standard 9×9 killer (sudokuleader.com). The cheat sheet's real power is in its "unique sum" cages: sums with only one possible combination, which you can fill in by sight.

How Killer Sudoku Works (Quick Refresher)

Killer Sudoku uses a normal 9×9 Sudoku grid, but instead of starting numbers, the grid is split into cages — irregular groups of cells outlined with dashed lines. Each cage has a small total printed in its top-left corner, and the digits inside the cage must add up to that total (puzzlemadness.co.uk).

The rules are:

1. Standard Sudoku rules apply. Every row, column, and 3×3 box must contain the digits 1–9 exactly once.
2. Cage digits sum to the cage total. The numbers inside each cage add up to the number printed in the cage's corner.
3. No digit repeats inside a cage. Even if two cells of a cage sit in different rows, columns, and boxes, they cannot hold the same digit.
4. Cages have 2 or more cells. One-cell cages are trivial — the cell simply equals the total.

Because there are no givens, you start with pure logic and arithmetic instead of scanning rows. That is where the cheat sheet comes in (puzzlemadness.co.uk).

The 45 Rule: The Single Most Useful Killer Technique

Every row, column, and 3×3 box in Sudoku contains the digits 1–9, and 1+2+3+4+5+6+7+8+9 = 45. So every complete row, column, or box always sums to 45.

Here's the classic application from PuzzleMadness: look at the bottom-right 3×3 box, which contains 4 cages adding to 16+7+10+4 = 37. Those cages cover 8 of the 9 cells in the box — so the remaining cell must be 45 − 37 = 8 (puzzlemadness.co.uk).

The cheat-sheet version of the rule:

• When cages almost cover a row, column, or box, subtract their totals from 45 to solve the leftover cell instantly (jigsawmake.com).
• An 8-cell cage inside a box is missing exactly the digit 45 − cage sum.
• A 9-cell cage always holds all nine digits (sum 45) (jigsawmake.com).

Unique-Sum Cages: Memorise These First

Across the full 502-combination chart, some sums have exactly one possible combination (marked • on most cheat sheets). The moment you see one of these on the board, you know precisely which digits live in the cage — only their order is unknown (sudokuleader.com). These are the highest-value facts on any killer Sudoku cheat sheet:

(sudokuleader.com; jigsawmake.com)

Memorising just these ten — plus the near-unique ones like 2-cell sum 5 (1+4 or 2+3) and 2-cell sum 15 (6+9 or 7+8) — covers the openings of most published killer puzzles.

2-Cell Cage Combinations (Sums 3–17)

The 2-cell table has only 36 combinations, making it the easiest section to internalise (sudokuleader.com):

(• = only one combination possible; sudokuleader.com)

Notice the symmetry: sums pair up around 10. If you know the low end, the high end mirrors it — a handy mental shortcut when you don't have the sheet in front of you.

3-Cell Cage Combinations (Sums 6–24)

The 3-cell table has 84 combinations. You don't need to memorise all of them — learn the unique ones and the general shape (sudokuleader.com):

Full 3-cell tables run from sum 6 (1+2+3) to sum 24 (7+8+9); middle sums like 14, 15, and 16 each have 8 possible combinations, which is why large cages are the hardest part of killer Sudoku (sudokuleader.com).

How to Use a Cheat Sheet While Solving

Start with the unique-sum cages

Pencil the digits of every unique-sum cage into its cells as candidates. A 2-cell cage totalling 17 is 8+9 — mark both cells {8,9} immediately and you've already constrained the row, column, and box (sudokuleader.com).

Use the 45 rule on nearly-covered units

Before touching combinations, scan every row, column, and box for cages that cover all-but-one cell. Subtracting from 45 gives you a certain digit — the strongest possible opening move (puzzlemadness.co.uk; jigsawmake.com).

Apply Sudoku logic inside cages

Cheat-sheet candidates are only the start. A 2-cell sum-9 cage could be 1+8, 2+7, 3+6, or 4+5 — but if its row already contains a 3 and a 7, only 1+8 and 4+5 survive, and Sudoku elimination does the rest. Always intersect cage possibilities with row, column, and box constraints.

Keep pencil marks disciplined

Mark only the candidates a cage's combinations allow, and update them as digits get placed. Overloaded cells slow you down; clean, current candidates let the naked-pair and hidden-single patterns surface naturally (conaemi.org.mx killer sudoku guide).

Use parity as a quick filter

An arithmetic shortcut many cheat sheets highlight: if a 2-cell cage sum is odd, its digits must be one even and one odd; if the sum is even, both digits share parity (both even or both odd). This instantly halves some candidate lists without consulting a table.

Printable Cheat Sheets and Combination Calculators

• Sudoku Leader — Killer Sudoku Calculator (sudokuleader.com). The complete 502-combination chart for cage sizes 2 through 9, with unique-sum rows highlighted — the most thorough online reference (sudokuleader.com).
• JigsawMake — Killer Sudoku Cheat Sheet A4 PDF (jigsawmake.com). A printable one-page A4 sheet covering 2-cell and 3-cell combinations plus the 45-rule shortcuts — ideal beside a paper puzzle (jigsawmake.com).
• PuzzleMadness — Killer Sudoku How to Play (puzzlemadness.co.uk). A worked walkthrough of the 45 rule with annotated example grids — the best tutorial for understanding why the techniques work (puzzlemadness.co.uk).

If you like the arithmetic side of puzzles, our sudoku puzzle book guide covers choosing printed collections, and the prize crossword clue article explains another classic British puzzle format. For word puzzles with a similar logic flavour, see What Is Parseword?.