Killer Sudoku Rules Explained: How Cages and Sums Work

The grid

Killer Sudoku uses the same 9x9 grid as Classic Sudoku — 81 cells in nine 3x3 boxes. On top of that grid, the puzzle overlays a set of cages: groups of neighboring cells outlined with a dashed border, each labeled with a small number in its top-left corner. That number is the sum every digit inside the cage must add up to.

The rules: standard, plus cages

Every Classic Sudoku rule still applies in full:

• • Each row contains 1–9 exactly once — no repeats.
• • Each column contains 1–9 exactly once — no repeats.
• • Each 3x3 box contains 1–9 exactly once — no repeats.

Killer Sudoku adds two more requirements on top of those three:

• • Every cage's digits must add up to its target sum — exactly, no more and no less.
• • No digit repeats inside a cage, even if the row, column, and box rules alone would allow it.

Cages can be almost any connected shape — a straight line, an L, a zigzag — and they often cross box and row boundaries freely. Most hold between two and five cells. What never changes is the arithmetic: sum up right, no repeats, every time.

A worked example: reading cage sums

Look at the two solved cages in the image above. The top-left cage holds 2 cells and sums to 3. Since digits can't repeat and every digit is between 1 and 9, the only pair of distinct digits that adds up to 3 is 1 and 2 — there's no other option, so both cells are solved the moment you read the cage label, before checking a single row or column.

The second cage holds 2 cells and sums to 17. At the opposite extreme, the only pair that reaches 17 without repeating a digit is 8 and 9. Sums near the low end (like 3) or the high end (like 17) of a 2-cell cage's possible range (3 through 17) tend to have exactly one valid combination, which makes them the fastest cages to solve on sight.

The two unlabeled cages further down — a 3-cell cage summing to 7, and a 2-cell cage summing to 4 — work the same way, just with a bit more to narrow down: a 3-cell cage summing to 7 can only be some arrangement of 1, 2, and 4, while a 2-cell cage summing to 4 can only be 1 and 3 (never 2 and 2, since digits can't repeat). Once you've listed a cage's possible digit sets, cross-check them against the row, column, and box rules the same way you would in Classic Sudoku to figure out which cell gets which digit.

Fast combinations worth memorizing

A handful of cage sums have only one possible digit combination, which makes them worth recognizing on sight:

• • 2-cell cage summing to 3 — must be 1 + 2.
• • 2-cell cage summing to 4 — must be 1 + 3.
• • 2-cell cage summing to 16 — must be 7 + 9.
• • 2-cell cage summing to 17 — must be 8 + 9.
• • 3-cell cage summing to 6 — must be 1 + 2 + 3.
• • 3-cell cage summing to 24 — must be 7 + 8 + 9.

Cages in the middle of the possible range (a 2-cell cage summing to 9 or 10, for example) usually have several valid combinations, which is where you'll lean more heavily on the row, column, and box rules to narrow things down. For the broader technique library those rules draw on, see our solving techniques guide.

Notes (pencil marks)

Because Killer Sudoku often gives you few or no pre-filled digits, notes matter more here than in most variants. A common approach is to jot every possible digit combination for a cage as candidates, then eliminate combinations as you cross-check them against the row, column, and box a cell belongs to. As with every variant, notes are just scratch space — only the digit you finally commit to a cell needs to satisfy every rule at once.

Difficulty levels

Unlike other variants, Killer Sudoku difficulty is driven mostly by how many pre-filled givens accompany the cages, not just the cage layout itself:

Common rule mix-ups

• • Assuming a digit can repeat in a cage if the sum still works — it can't; 2+2=4 is arithmetically valid but illegal in a 2-cell cage because the digits repeat.
• • Expecting cages to respect box boundaries — they don't. A single cage can span two or three different 3x3 boxes.
• • Forgetting the standard rules still apply — solving a cage's arithmetic doesn't override the row, column, and box rules; a digit still needs to satisfy all of them at once.
• • Treating every cage sum as ambiguous — sums at the extreme ends of a cage's possible range (very low or very high for its cell count) often have exactly one valid combination, worth spotting immediately.

Frequently asked questions