Killer Sudoku

Killer Sudoku

Every rule of Classic Sudoku, plus cages — dashed groups of cells with a target sum and no repeated digit. That single addition turns the puzzle into an arithmetic one.

In short

Killer Sudoku is Classic Sudoku with cages: dashed groups carrying a target sum, inside which no digit may repeat. Boards usually start with no given digits at all, so every deduction begins from the cage totals rather than from printed numbers.

The rules

Killer Sudoku keeps all three Classic rules intact. Fill the 9×9 grid so that every row, every column and every 3×3 box holds the digits 1 to 9 exactly once. Nothing about that changes.

On top of it sits one extra rule. The grid is divided into cages — groups of cells marked by a dashed outline, each printed with a small target sum in its top-left corner. The digits in a cage must add up to that sum, and no digit may repeat inside a cage. A cage can be any shape and can cross box boundaries freely.

The no-repeat rule inside a cage is what makes the puzzle tractable. Without it a 3-cell cage totalling 23 could be 5+9+9, and almost no total would tell you anything. With it, 23 in three cells can only be 6+8+9 — a single possibility, handed to you before you place a digit.

Starting from nothing

The biggest practical difference from Classic is that Killer boards on this site begin with zero given digits. There is no printed 7 to scan from. The only information on the board is the cage geometry and the sums, so the opening move is always arithmetic rather than scanning.

That sounds harder than it is. Cage sums are extremely informative: a 2-cell cage totalling 3 can only be 1+2, and a 4-cell cage totalling 30 can only be 6+7+8+9. An experienced solver opens by sweeping the board for exactly those forced totals, which pins whole groups of cells before anything else happens.

Once a few cages are pinned, Killer collapses back into Classic. The naked singles, hidden singles, locked candidates and subsets you already know do most of the remaining work — the cage techniques simply keep feeding them.

The cage vocabulary

A combination is one of the digit sets that could fill a cage of a given size and sum. A 3-cell cage totalling 7 has exactly one combination, {1,2,4}; one totalling 15 has eight. Listing the combinations and discarding the impossible ones is the central Killer skill.

An innie is a cell inside a row, column or box that no fully-contained cage covers; an outie is a cell of a cage that pokes out beyond the unit being analysed. Both come from the Rule of 45 — every unit holds 1 to 9 exactly once and so sums to 45, and comparing 45 against the cages covering that unit reveals what the leftover cells must total.

The full vocabulary, including terms shared with Classic, is in the Sudoku glossary.

The six techniques, in order

The lessons below are ordered by the tier at which each technique first becomes necessary. Each walks its deduction on a real board through the same Next-Step teacher the in-game hint uses, followed by a written companion with worked examples and diagrams.

The Killer Lessons

Frequently Asked Questions

How is Killer Sudoku different from regular Sudoku?

Killer keeps every Classic rule and adds cages: dashed groups of cells with a target sum, inside which no digit may repeat. Killer boards also usually start with no given digits, so the first deductions come from cage arithmetic rather than from scanning printed numbers.

Can a Killer cage contain the same digit twice?

No. Every digit inside a cage must be different, which is what keeps combination lists short and makes cage totals informative. Without the rule a 3-cell cage totalling 23 could be 5+9+9 as well as 6+8+9, and almost no total would force a single set.

Do Killer Sudoku puzzles have any given numbers?

Killer puzzles on this site start with none at all. The cage outlines and their sums carry all the information you need, and the opening move is to find cages whose size and total admit only one digit set.

What about cages with 8 or 9 cells?

An 8-cell cage is always forced: eight distinct digits are 1 to 9 with one missing, and the missing digit is 45 minus the total, so every total from 36 to 44 gives a single set. A 9-cell cage must total 45 and hold 1 to 9. Both are really Rule of 45 deductions.

Do cage techniques tell you which cell each digit goes in?

Usually not. Cage techniques fix the set of digits a cage holds, not their arrangement. A 3-cell cage totalling 23 must hold 6, 8 and 9, but any of the three could sit in any of the three cells. Placement follows when a row, column, box or neighbouring cage rules out the alternatives.

Do I need to memorise cage combination tables?

No, though a few are worth knowing. The forced totals are the two lowest and two highest each cage size can reach — 3, 4, 16 and 17 for two cells; 6, 7, 23 and 24 for three. Those are where a scan pays off. The rest can be worked out when you need them.

Are Killer Sudoku puzzles harder than Classic?

Not inherently, though the opening feels stranger with no givens to scan. Killer puzzles here are graded on the same five tiers as Classic, and an Easy Killer is genuinely easy once you can spot a forced cage. The arithmetic is addition only, never anything more.

Keep Going

Every Classic technique still applies in Killer — see the Learning Hub for all 28, or the glossary for the full vocabulary. New to Sudoku entirely? Start with how to play.