How do you play Killer Sudoku?

The rules of Killer Sudoku

There are only four rules, and three of them you already know from classic sudoku:

• Rows, columns, and boxes work as usual. Each row, each column, and each 3×3 box contains the digits 1–9 exactly once. Nothing about killer suspends this — a cage-sum deduction that breaks a row is wrong.
• Every cage must total its printed sum. A cage marked 15 spanning three cells needs three digits adding to exactly 15 — no more, no less.
• Digits never repeat within a cage. A two-cell cage summing to 10 cannot be 5+5; it must be 1+9, 2+8, 3+7, or 4+6. This holds even when a cage snakes across two boxes or bends around a corner — the cage itself forbids the repeat, regardless of what the rows and columns would allow.
• There are usually no given digits. Where a classic puzzle hands you 25–30 starting clues, a killer grid is typically blank. The cage sums replace the givens entirely, which is why the first few minutes of a killer puzzle feel so different: you start by doing arithmetic, not by scanning for near-complete rows.

That last point is worth sitting with. Because digits can't repeat in a cage, each cage sum corresponds to a short list of possible digit sets — and some sums have exactly one. A two-cell cage marked 17 must be 8 and 9. You don't know which cell holds which yet, but you've already eliminated seven digits from both cells before placing anything. Killer solving is largely the craft of stacking these little certainties until digits fall out.

The 45 rule: the one technique you must know

The digits 1 through 9 add up to 45. Since every row, every column, and every 3×3 box contains each digit exactly once, every row, column, and box in the grid sums to exactly 45. That single fact is the engine behind most killer deductions, and it's called the 45 rule.

Here's how you use it. Find a box (or row, or column) that is almost perfectly tiled by cages — where the cages covering it either poke one cell out of the region, or leave one cell of the region uncovered. Then it's simple arithmetic:

Worked example (an "outie"): suppose the cages lying over the top-left box have sums 14, 11, 8, and 15 — a total of 48 — and exactly one cell of the 15-cage sticks out into the neighboring box. The nine cells of the box must sum to 45, so the one cell sticking out must account for the difference: 48 − 45 = 3. You just placed a digit in a blank grid without a single given clue.

The mirror case (an "innie"): if the cages contained entirely within a box sum to 41 and leave exactly one cell of the box uncovered, that cell must be 45 − 41 = 4.

The rule scales. Two rows together sum to 90, three to 135, and the whole grid to 405 — so a pair of cells poking out of a two-row band is a two-cell "cage" whose sum you've computed yourself, complete with the no-repeat property if both cells share a row or box. Strong solvers spend their first pass over a killer grid hunting innies and outies before they touch a single cage.

Starting strategy: where the first digits come from

A blank killer grid looks intimidating, but the opening is more mechanical than a classic puzzle. Work in this order:

• Extreme cages first. Scan for the cages whose sums have only one possible digit set: two-cell cages of 3 (1+2), 4 (1+3), 16 (7+9), and 17 (8+9); three-cell cages of 6 (1+2+3), 7 (1+2+4), 23 (6+8+9), and 24 (7+8+9). Pencil-mark those candidates immediately — they're facts, not guesses.
• Smallest cages next. Two-cell cages rarely have more than four combinations, so they respond fastest to eliminations. When a 10-cage sits in a row that already contains a 1, it collapses from four combinations to three.
• Run the 45 rule over every box, then rows and columns. Any region with a single innie or outie hands you a solved cell or a tight two-cell sum. Even regions with two-cell innies are worth noting — a self-made two-cell sum of 5 or 16 is nearly as strong as a printed cage.
• Cross-reference cages against regions. A three-cell 24-cage (7+8+9) inside one box means no other cell of that box can hold 7, 8, or 9. Cage knowledge and sudoku knowledge multiply each other — this interplay is the whole game.
• Only then fall back on classic techniques. Once a handful of digits are placed, killer becomes regular sudoku with extra constraints: naked pairs, pointing candidates, and box/line reduction all apply exactly as they do in classic.

One habit matters more in killer than anywhere else: use pencil marks from the very first move. Cage combinations are candidate lists by nature; trying to hold "this cage is 2+8 or 3+7, and that one is 1+5 or 2+4" in your head across a 40-minute solve is how mistakes happen.

Is Killer Sudoku harder than Classic?

Honest answer: it depends on which techniques you've built, because the two variants are hard in different ways.

An easy killer puzzle is arguably more approachable than an easy classic: the opening moves are arithmetic anyone can do (find the 17-cage, apply the 45 rule), while classic sudoku asks you to spot visual scanning patterns that take practice to see. Plenty of people who bounced off classic sudoku find killer clicks for them precisely because the logic is written on the grid as numbers.

At the hard end, killer gets brutal in its own way. With no givens and generous cage sums (a five-cell 25-cage has twelve possible digit sets), difficult killers demand combination bookkeeping on top of the advanced classic techniques. The hardest killers are widely considered tougher than the hardest classics simply because they stack both skill sets.

The practical takeaway: don't map your classic difficulty level across directly. If you solve Hard classics comfortably, start killer at Easy or Medium, learn the cage-combination instincts, and climb from there. The difficulty ladder in a good app exists exactly for this — in Sudoku by Joseph, killer runs the same Easy–Diabolic range as every other variant.

Solving your first Killer sudoku in Sudoku by Joseph

1. Install the app

   Download Sudoku by Joseph for iPhone, iPad or Android. Killer sudoku is included in the free tier alongside Classic and Jigsaw — no purchase needed to follow this guide.

2. Pick Killer, set difficulty to Easy

   Choose Killer from the variant chooser and start on Easy, even if you play harder classics. Easy killers have small cages and several single-combination sums, which is exactly what you want while the cage logic is new.

3. Open with cage-sum logic

   Before entering anything, scan for extreme cages (two-cell 3, 4, 16, 17; three-cell 6, 7, 23, 24) and pencil-mark their forced digits. Then check each 3×3 box for an innie or outie and apply the 45 rule.

4. Pencil-mark every cage you touch

   Keep candidate lists in notes rather than your head. Each digit you place shrinks the combinations of every cage it sees — re-scan the affected cages after each placement, and the grid unravels. There is no mistake counter, so a wrong deduction costs you nothing but the trace-back.

Practical tips for new killer solvers

• Memorize the eight extreme cages (2-cell: 3, 4, 16, 17; 3-cell: 6, 7, 23, 24) — they are the killer equivalent of knowing your times tables.
• When a cage has two combinations sharing a digit, that digit is certain even though the rest is not: a two-cell 16 or a three-cell 23 both lock a 9 somewhere in the cage.
• Big middling cages (four cells summing 18–22) have the most combinations — leave them for last and let the grid shrink them for you.
• A cage confined to one row, column, or box exports its digits as eliminations to the whole region; a cage spanning two boxes exports far less. Check the geometry before you lean on a cage.

Other options worth knowing

Good killer resources beyond this site: SudokuWiki's killer strategy pages go deep on advanced cage techniques and are the standard reference for the theory. DailyKillerSudoku.com publishes free browser puzzles every day with a clean interface. BrainBashers offers daily killers plus a printable combination chart. If you'd rather have combinations computed for you as you solve, our own interactive cage-combination calculator covers every cage size and sum. And if you want killer on your phone with pencil marks, hints on request, and no lives or mistake counters, that's what Sudoku by Joseph is for — killer is free in the app.

Frequently asked questions