Killer Sudoku Rules

What is Killer Sudoku?

Killer Sudoku (also called "Sum Sudoku" or "Samunamupure") is a Sudoku variant invented in the 1990s that combines the classic 9x9 logic puzzle with arithmetic. Instead of starting with given digits, you start with an almost-empty grid divided into dotted regions called cages, each marked with a small sum.

Your job is to fill the grid following all the classic Sudoku rules — and on top of that, make sure each cage's digits add up to the printed sum, without repeating any digit inside the cage.

The three rules, plainly

1. Classic Sudoku rules apply. Every row, every column, and every 3x3 box must contain the digits 1 through 9, each exactly once.
2. Cage sums must match. The digits inside each dotted cage must add up to the small number printed in the top-left corner of the cage.
3. No repeats inside a cage. A digit cannot appear twice in the same cage, even if the cage spans multiple rows or boxes.

That's it. If you can solve a classic Sudoku, you already know two-thirds of Killer Sudoku. The arithmetic is just an extra layer of clues.

What does a cage look like?

A cage is a group of orthogonally connected cells outlined by a dashed border. Cages can be any shape: a single cell, a domino of two, an L-shape, a T-shape, or larger irregular blobs. The sum is written in the top-left cell of the cage in small print.

For example, a cage of two cells with the clue "7" means those two cells contain digits adding to 7 (and not repeating each other): one of 1+6, 2+5, or 3+4. A single-cell cage with clue "5" just means that cell is 5 — already solved before you started.

The Rule of 45 (your most powerful tool)

Here's what turns Killer Sudoku from intimidating to solvable: in any classic Sudoku unit (row, column, or 3x3 box), the digits 1 through 9 each appear exactly once. And 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

So the cages inside any row, column, or box must add up to exactly 45. This is called the Rule of 45, and it lets you deduce missing cage values, pin down stray cells, and solve cages that have no internal logic at all.

Example: Suppose a row contains three cages summing to 9, 16, and 13 entirely inside the row, plus one cage that spills out — its in-row portion is two cells, and the cage's total is 14 with one cell outside the row. The in-row part must be 45 − 9 − 16 − 13 = 7. So the two in-row cells of that cage sum to 7, and the spilled cell is 14 − 7 = 7. Done — without trying any digit combinations.

Three starting strategies for beginners

1. Unique sums

Some cage sums have only one possible combination of digits. These are gold:

• Two cells summing to 3 → must be 1+2
• Two cells summing to 4 → must be 1+3
• Two cells summing to 16 → must be 7+9
• Two cells summing to 17 → must be 8+9
• Three cells summing to 6 → must be 1+2+3
• Three cells summing to 7 → must be 1+2+4
• Three cells summing to 23 → must be 6+8+9
• Three cells summing to 24 → must be 7+8+9

When you spot one of these, you immediately know which digits the cage contains — even if you don't yet know which digit goes in which cell. That's usually enough to eliminate those digits from the rest of the row, column, or box the cage sits in.

2. Cages locked inside a single unit

If a cage of three cells lies entirely within one 3x3 box, those three digits are also confined to that box. So if the cage must be {1, 2, 4}, you can remove 1, 2, and 4 from every other cell in the box — the same logic as a Naked Pair, just with three digits.

The same is true for cages locked inside a single row or column. Always check whether a cage fits inside one unit — that constraint propagates strongly.

3. Innies and Outies (the Rule of 45 in action)

An innie is a single cell that "sticks into" a row, column, or box from outside; an outie is a single cell that pokes out. Both can be solved with subtraction: add up the cages fully inside the unit, compare to 45, and the difference is the innie or outie's value.

These are usually the very first moves expert solvers make on a fresh Killer puzzle — and they often crack the whole grid open.

Killer Sudoku vs. classic Sudoku

• Classic Sudoku gives you 20–35 starting digits and asks you to fill the rest using only positional logic.
• Killer Sudoku gives you zero starting digits but provides dozens of arithmetic clues. The grid is harder to enter but richer in deductions once you learn to read the cages.
• All classic techniques — Naked Singles, Hidden Singles, Naked Pairs — still apply. Killer Sudoku just adds arithmetic on top.

Common beginner mistakes

• Repeating digits in a cage. Even if a cage of two summing to 10 could mathematically be 5+5, that's not allowed — digits inside a cage must be different.
• Ignoring the Rule of 45. Beginners often try to crack cages one at a time. Stepping back to apply Rule-of-45 across a whole row or box usually finds moves nothing else can.
• Forgetting classic constraints. Cage sums are extra clues, not replacements. A cage of {1, 3} still has to obey the no-repeat rule for its row, column, and box.
• Mistaking the sum location. The sum is always in the top-left cell of the cage. If you see a small number, it's a cage clue, not a candidate note.

Try it yourself

SudokuHint currently focuses on classic Sudoku — but the techniques you build there transfer directly to Killer. Start with an easy classic puzzle to lock in the basic patterns (Naked Singles, Hidden Singles, scanning), then come back to Killer with a stronger foundation. Killer Sudoku support is on the roadmap.

Article draft v1 · pending native-speaker review