Killer Sudoku Combinations Cheat Sheet: All Cage Sums

What Are Killer Sudoku Cage Combinations?

Killer sudoku layers a second rule on top of classic sudoku: the grid is divided into “cages”—groups of two or more cells outlined with a dotted border, each labeled with a target sum. Every cage must contain digits that add up to that sum, and just like a row, column, or 3x3 box, no digit can repeat within a cage.

That single constraint is what makes killer sudoku combinations the fastest way into a puzzle. Instead of guessing, you can work out exactly which digits are mathematically allowed to sit in a cage before you even look at the rest of the grid. This killer sudoku combinations cheat sheet lists every possible combination for every cage size from 2 to 9 cells—502 combinations in all—so you can check candidates in seconds instead of doing mental arithmetic mid-solve.

Jump to a table: 2-cell · 3-cell · 4-cell · 5-cell · 6–9 cell · required digits

Printable Killer Sudoku Cheat Sheet (Free PDF)

Prefer a copy next to your puzzle? Download the condensed cheat sheet as a free printable PDF—the 45 rule, full 2-cell and 3-cell tables, every unique cage from 2 to 9 cells, and the most useful required digits on a single reference sheet. No sign-up, no watermark.

The 45 Rule: Your First Tool

Before you touch the combination tables, learn the 45 rule. Every row, column, and 3x3 box in a standard sudoku grid contains the digits 1 through 9 exactly once, and 1+2+3+4+5+6+7+8+9 = 45. That means the digits in any complete row, column, or box must always sum to 45—no exceptions.

This becomes a solving weapon whenever a set of cages lines up almost perfectly with a row, column, or box, but one cell sticks out or one cell is missing. Subtract the known cage totals from 45 and the leftover single cell is solved instantly.

For example, imagine a box is covered by three cages summing to 14, 12, and 15, plus one extra cell that belongs to a cage outside the box. The three cages account for 14 + 12 + 15 = 41 of the box's cells. Since the whole box must total 45, that leftover cell is worth 45 − 41 = 4. No candidates, no trial and error—just subtraction.

2-Cell Cage Combinations

Two-cell cages are the building blocks of most killer sudoku puzzles. Here is every possible combination for sums 3 through 17, with the unique combinations (sums that only have one possible pair of digits) called out.

Sums of 3, 4, 16, and 17 are the ones worth memorizing first. The moment you spot a 2-cell cage totaling one of those four numbers, you already know both digits—you just need to work out which cell gets which value.

3-Cell Cage Combinations

Three-cell cages have more possible combinations in the middle of the range, but the extreme sums still lock down to a single answer. Here is the full list for sums 6 through 24.

Just like the 2-cell table, focus your memory on the edges: sums of 6, 7, 23, and 24 each resolve to exactly one combination of digits.

4-Cell Cage Combinations

Four-cell cages run from a sum of 10 up to 30, with 126 combinations in total. The middle of the range is crowded—a sum of 20 alone has 12 possible combinations—so during a solve you will usually scan this table to eliminate candidates rather than memorize it. The four unique sums (10, 11, 29, and 30) are still worth knowing by heart.

5-Cell Cage Combinations

Five-cell cages mirror the 4-cell pattern: 126 combinations across sums 15 through 35, dense in the middle and locked at the extremes. Sums of 15, 16, 34, and 35 each have exactly one combination.

6-Cell to 9-Cell Cage Combinations

Large cages look intimidating, but there is a shortcut: think in terms of the digits that are missing. A 6-cell cage is just the nine digits minus three of them, so a 6-cell cage summing to S contains exactly the digits left over from a 3-cell group summing to 45 − S. A 7-cell cage is the complement of a 2-cell group, an 8-cell cage is the complement of a single digit (45 minus the sum tells you which digit is missing), and a 9-cell cage always contains all nine digits and always sums to 45.

That complement trick means you can solve any large cage with the small tables above. The full lists are here for quick reference:

Every 8-cell cage is unique—the sum immediately identifies the one missing digit (45 minus the sum):

Required Digits: Sums That Force a Number

Even when a cage has several possible combinations, some digits appear in every one of them—so they must be somewhere in that cage no matter which combination turns out to be correct. These required digits are one of the fastest candidate-elimination tools in killer sudoku, and most cheat sheets skip them entirely. The table below lists every cage size and sum with two or more combinations that still forces at least one digit.

Read it like this: every 3-cell cage summing to 8 must contain a 1 (its combinations are 1+2+5 and 1+3+4—both include 1). If that cage sits in a row where the 1 is already placed elsewhere, you have an immediate contradiction to exploit.

How to Use This Cheat Sheet While Solving

Knowing the combinations is only half the job. Here is the order of operations top killer sudoku solvers actually use during a puzzle:

1. Scan for unique-combination cages first. Every sum marked “unique” in the tables above—2-cell cages totaling 3, 4, 16, or 17, 3-cell cages totaling 6, 7, 23, or 24, the 4-cell and 5-cell extremes, and every 8-cell cage—gives you locked-in digits before you've solved anything else.
2. Apply the 45 rule to define single cells. Whenever cages nearly cover a full row, column, or box, subtract their totals from 45 to solve the leftover cell directly.
3. Check required digits before candidates. If the cage's size and sum appear in the required digits table, pencil that digit into the cage immediately—it holds no matter which combination is correct.
4. Cross-reference combinations to eliminate candidates. When two overlapping cages share a possible digit in only one of their combination lists, you can rule that digit out of the other cells in the grid.
5. Layer in standard sudoku technique. Once cage logic narrows your candidates, switch back to normal scanning, naked pairs, and other row/column/box techniques to finish the puzzle. Practice this combined approach on our hard sudoku generator, or build your own custom difficulty puzzles with the sudoku puzzle maker.

Practice Makes Permanent

The combinations above will start to feel automatic after a handful of puzzles, but only if you actually put them to work. Sketch your own killer cages onto a printed grid by hand, and try solving with nothing but this cheat sheet and the 45 rule—hand-drawing a few cages is one of the fastest ways to make the unique combinations stick in memory.

Once cage combinations feel natural, round out your solving toolkit with our sudoku solving strategies guide, which covers the classic scanning and elimination techniques that carry you through the rest of any killer sudoku grid.

Frequently Asked Questions