➕ Killer Sudoku Puzzles

Killer Sudoku: A Sudoku Grid With Nothing Written In It

Open an ordinary Sudoku and somebody has already done a bit of the work for you — twenty-odd digits are sitting there waiting. Open a Killer Sudoku and the grid is completely, alarmingly blank. What you get instead is a patchwork of coloured blocks called cages, each with a small number tucked in its top-left corner telling you what the digits inside it add up to. Newspapers print those cages as dotted outlines because they only have one ink; on screen we can just give each one its own shade, and neighbouring cages never share a colour.

The first time you see one it looks like there's nothing to grab hold of. There is. The sums are the clues, and a few of them are so restrictive that they may as well be printed digits.

📏 The Three Rules

1. Everything you know about Sudoku still applies. Every row, every column and every box holds each digit exactly once — 1 to 9 on the big grid, 1 to 6 on the 6 × 6, 1 to 4 on the 4 × 4.
2. Each cage adds up to its corner number. A cage is just a group of connected cells; the little number belongs to the whole cage, not to the cell it happens to sit in.
3. A digit can't repeat inside a cage. This one matters more than it looks. A cage that straddles two boxes could hold two 6s as far as the Sudoku rules are concerned — but the cage rule forbids it anyway.

That third rule is doing a great deal of quiet work. It's the reason a cage's total maps onto a small, knowable set of digit combinations rather than a vague "some numbers that add up".

🧮 Where the Starting Numbers Went

Here's the swap Killer Sudoku makes: instead of giving you a couple of dozen digits, it gives you roughly the same number of sums, and lets arithmetic do the rest.

Ask what a cage's total could be made of. Two cells totalling 17? The only pair of different digits that reaches 17 is 8 and 9 — so those two cells are an 8 and a 9 in some order, and no other cell in their row, column or box can be an 8 or a 9 if they share one. Two cells totalling 3? That's 1 and 2, with no alternative at all.

Compare that with a two-cell cage totalling 9, which could be 1+8, 2+7, 3+6 or 4+5. Same puzzle, same cage size, and it tells you almost nothing. Learning which sums are generous and which are stingy is most of the skill in this game.

You'll also spot the odd cage of a single cell. That's the one case where the sum is the answer — a lone cell marked 6 contains a 6 — and it's as close as Killer Sudoku ever gets to handing you a given. Easy and Medium grids always include a few (three and two respectively on the 9 × 9), because a free digit is a place to start. Hard grids have none: you break in with arithmetic or not at all.

🔓 The Sums With Only One Answer

These are the cages worth hunting for the moment a fresh 9 × 9 grid appears. Each of these totals can be made in exactly one way:

The pattern is easier to remember than the table: the very smallest total for a cage is always the digits 1, 2, 3… packed in from the bottom, and the very largest is 9, 8, 7… packed in from the top. One step in from each end is still unique, because there's only one digit you can nudge. Two steps in and the alternatives start appearing.

On our 6 × 6 grid the same idea holds with a shorter alphabet: two cells totalling 3 must be 1+2 and two totalling 11 must be 5+6, while a three-cell cage totalling 6 is 1+2+3 and one totalling 15 is 4+5+6.

The other half of this is knowing when a cage can't exist in a shape you assumed. A five-cell cage can never total less than 15 or more than 35, so a big cage with a small-looking number is often the most informative clue on the board — a 5-cell cage marked 16 is nearly pinned down before you've written anything.

➗ The Rule of 45

This is the technique that makes Killer Sudoku its own game rather than Sudoku with decoration, and it's the one our Hard puzzles are built around.

Every box on a 9 × 9 grid contains the digits 1 to 9 once each. So every box totals 45. So does every row and every column. Now look at a box where the cages almost line up with its edges:

That leftover cell is called an innie. You've just read a digit off the grid without knowing a single thing about the cage it belongs to. The mirror-image move is the outie: take every cage that has at least one cell in a box, add all their totals, and if exactly one of their cells pokes out beyond the box, that cell equals the running total minus 45.

The rule scales, too. Two whole rows total 90; three total 135. On a big grid it's often the only way to break in once the easy cages have been used up, and it's the move to reach for whenever you're stuck and everything left looks like a mush of maybes.

On our smaller boards the number changes but the trick doesn't: a 6 × 6 row, column or box totals 21, and a 4 × 4 one totals 10.

🧱 Cages That Live Inside One Box

A cage tucked entirely within a single box, row or column is worth more than one that sprawls. If a three-cell cage marked 7 sits inside one box, then 1, 2 and 4 are all spoken for in that box — you can strike them out of the other six cells immediately, without knowing which of the three cage cells holds which.

None of our puzzles force you to use this one — the sums and singles will get you there — but it is the fastest shortcut on the board, and on a Hard grid it's usually what sets up the rule-of-45 deduction that follows. It also explains why cage shape matters as much as cage size: a long snaking cage that wanders through three boxes gives you a sum and very little else, while a compact square cage of the same size can gut a whole box.

🪜 An Opening Routine That Works

1. Scan for the one-answer cages first. Every 17, 16, 3 and 4 on a pair of cells; every 6, 7, 23 and 24 on a trio. Pencil the forced digits into your head before you write anything.
2. Then find the cages that live inside one box. Each one hands you a set of digits to remove from the rest of that box.
3. Now do a 45 sweep. Walk the boxes, then the rows, then the columns, adding up the cages that fit neatly inside. Any single leftover cell is a free digit.
4. Only now start on ordinary Sudoku singles. Once a few digits are down, the usual "this is the only cell in the row that can hold a 4" reasoning takes over — and every digit you place shrinks the possible combinations of the cage it lives in.

🚧 What Sudoku and Kakuro Players Get Wrong

• Waiting for something to be given. Sudoku players often stare at the blank grid looking for the usual foothold. There isn't one. The foothold is a cage total, and you find it with the combination table, not by scanning rows.
• Forgetting the cage rule at box borders. The single most common slip: a cage crosses from one box into the next, and both halves get the same digit. The Sudoku rules allow it; the cage rule doesn't. Our grid turns the whole cage red the moment that happens.
• Assuming Kakuro habits transfer cleanly. They mostly do — Kakuro's runs and Killer's cages share the "no repeats, hit the total" idea. But a Kakuro run is always a straight line, so it always sits in exactly one row or one column. A Killer cage can be an L, a T or a zigzag, and which houses it touches changes what it's worth. Check the shape, not just the number.
• Treating a big cage as bad news. A five-cell cage looks intimidating and is often the friendliest thing on the board, because extreme totals for large cages are far more restrictive than extreme totals for small ones.
• Adding up carelessly. Unlike most logic puzzles, an arithmetic slip here doesn't just cost you a cell — it quietly poisons every deduction downstream. Recount a cage before you trust it.

🎚️ Sizes and Levels on This Page

Three grid sizes, and they're genuinely different puzzles rather than the same one scaled:

• 4 × 4 — digits 1 to 4, boxes of four cells, and every row, column and box totals 10. Six or seven cages, no total higher than 10. A complete Killer Sudoku in a minute or two, and the gentlest possible introduction to reading a cage.
• 6 × 6 — digits 1 to 6 in 2 × 3 boxes, totalling 21. Around seventeen cages on Easy, down to about eleven on Hard. Big enough for the rule of 21 to be worth using, small enough to finish over a cup of tea.
• 9 × 9 — the real thing: 1 to 9, boxes of nine, and the rule of 45. Roughly forty cages on Easy, tightening to about twenty-five on Hard.

The three levels change which techniques you'll need, not just how many cages there are:

• Easy 😊 — cages of at most three cells and about forty of them on the big grid, most of them just two cells, so the combination table does nearly all the work. Three cages are a single cell each: free digits, and an obvious place to begin. Solvable start to finish on cage sums plus ordinary Sudoku singles.
• Medium 🤔 — the same two techniques, but a good deal more work. Cages run up to four cells, there are around thirty-two rather than forty, and only two free digits. A four-cell cage has far more ways to make its total than a two-cell one, so you weigh more possibilities per clue and the chains between them get longer.
• Hard 🧠 — cages up to five cells, about twenty-five in all, and nothing given away. These are built so that the combination work and the ordinary Sudoku techniques both run out, and the only way through is the rule of 45. If you're stuck on a Hard grid, start adding up boxes.

Two honest caveats. Easy and Medium ask for the same techniques — the step between them is how much grid you're given and how big the cages get, not a new idea to learn. That's deliberate: Killer's deductions run in a chain from wherever you first break in, so a puzzle that needs a harder technique anywhere tends to need it almost straight away. There is no gentle way to ask for a little more.

And the 4 × 4 board is too small for the deeper techniques at all. Sixteen cells and four digits leave no room for the rule of 10 to bite, so there the three levels change the cage sizes — up to four cells on Hard — rather than the reasoning. Come to 6 × 6 or 9 × 9 for a Hard that means it.

🎮 Playing on This Page

• Click or tap a cell and a keypad appears offering only the digits that still fit — anything that would repeat in the row, column, box or cage, or push the cage past its total, is left out.
• Use the keyboard if you'd rather: arrow keys to move around, a number key to place a digit, Backspace or Delete to clear one, and N to flip in and out of Notes.
• Notes ✏️ is worth turning on early. With it lit, tapping a number pencils it into the corner of the cell instead of committing to it, and the keypad stays open so you can jot a whole combination in one go — exactly what you want when a cage says 17 and you know it's an 8 and a 9 but not yet which way round. Notes accept any digit, even ones the grid currently rules out, because half the point is recording a maybe. Writing a real digit clears that cell's marks; nothing else touches them, so a wrong guess never wipes your working.
• On a phone, the number strip above the grid acts on whichever cell you've selected, and respects Notes mode too.
• Selecting a cell shades its whole cage, which is handy when a cage wanders across a box border and you've lost track of where it goes.
• Mistakes light up red straight away — a repeated digit, a cage that's already overshot its total, or a full cage with the wrong sum.
• Hint 💡 fills in one correct cell and flashes it orange. Solution ✅ reveals the finished grid, which is the fastest way to understand a cage that beat you.

🌏 Where Killer Sudoku Came From

Killer Sudoku is a genuine hybrid: the grid and the row-column-box rules come from Sudoku, and the summed groups with no repeated digits come straight from Kakuro. Unusually for a puzzle this popular, nobody is credited with inventing it — it emerged in Japanese puzzle magazines, where it's known as samunamupure, a squashing-together of "sum" and the Japanese shorthand for "number place".

It reached English-speaking players in 2005, when The Times in London began printing it as Killer Su Doku at the height of the Sudoku boom. The name stuck, which is a little unfair on a puzzle that is really just Sudoku with better clues. You'll also find it sold as Sumdoku, Sum Doku and Addoku, all of which describe it more accurately and none of which caught on.

🧒 Why It Suits Younger Players

We test these with children as well as adults, and the small grids land better than we expected:

• The sums are tiny. On the 4 × 4 board no cage total goes above 10, and most cages are just two cells. It's arithmetic practice that doesn't feel like a worksheet.
• Addition has an obvious purpose. The sum isn't the answer — it's a clue about which digits exist. That's a genuinely different way of using a number, and children pick it up quickly.
• The keypad teaches the rules. Because it only offers digits that still fit, a child can work by elimination long before they can articulate why a digit is impossible.
• Errors are immediate and reversible. A clash turns red the moment it happens, so the grid corrects rather than punishes.
• A 4 × 4 finishes fast. Sixteen cells and a handful of cages is a complete, satisfying puzzle — which matters when you're building the habit.

🚀 Give It a Go

Start on 6 × 6 Easy if you've never seen a cage before, or go straight to 9 × 9 Medium if you're a regular Sudoku solver. Either way, the first move is the same: find the smallest cage on the board and ask what its total could possibly be made of. Everything else follows from there. ➕