Summary: Killer sudoku takes a normal sudoku and hides the clues inside arithmetic. Instead of a scatter of given digits, the grid is carved into dashed cages, each printing the total its digits must add up to. This guide covers the goal, the rules that make every board solvable by pure logic, the cage-combination tricks that get you started, and where to try one in your browser.
Killer sudoku is a sudoku variant in which the grid is divided into dashed cages, each printing a total its digits must add up to, with no digit repeated inside a cage. The cages are the clues. You alternate between two kinds of thinking: the sums tell you which digits live inside a cage, ordinary sudoku tells you which cell each one lands in, and every digit you place shortens the next cage’s list.
The classic form goes further and prints no starting digits at all. The whole board is deduced from the sums.
The Goal
Fill every cell with a digit so that each row, each column and each heavy-outlined box holds every digit exactly once, and every dashed cage adds up to its printed total.
On a 9×9 board the digits are 1 to 9 and the boxes are the familiar 3×3 blocks. On a 6×6 board the digits are 1 to 6 and the boxes are two cells tall by three cells wide.
Killer Sudoku Rules
- Standard sudoku still applies. Every row, every column and every box contains each digit exactly once. The cages are added on top of that, never instead of it.
- Each cage adds up to its printed total. The small number in a cage’s top-left corner is the sum of every digit inside that cage.
- No digit repeats inside a cage. This is the rule that turns a sum into a real clue. A three-cell cage totalling 6 cannot be 2+2+2 — it can only be 1+2+3, in some order.
- Cages are two to five cells. They are always connected, they never overlap, and every single cell on the board belongs to exactly one of them. A cage can straddle two boxes, and many do.
- There is exactly one solution. Every board is checked for uniqueness before it is ever printed, so you never have to choose between two valid answers.
- You never have to guess. Each puzzle is confirmed solvable by human technique alone, at exactly the difficulty it claims. If you are stuck, there is a deduction you have not found yet — not a coin to flip.
- Easier levels print some digits too. The gentler difficulties fill in a handful of cells before you start, so there is a foothold to work from. The hardest levels are usually the pure form: cages only.
How to Solve Killer Sudoku: Six Steps
- Start from the extremes. Because a cage’s digits cannot repeat, a cage of N cells has a smallest and a largest possible total. On a 9×9 board a two-cell cage can only total between 3 and 17, a three-cell cage between 6 and 24, a four-cell cage between 10 and 30, and a five-cell cage between 15 and 35. On a 6×6 board, where the digits stop at 6, those ranges are 3–11, 6–15, 10–18 and 15–20. Sums at the ends of a range have almost no combinations: a two-cell 3 has exactly one, a two-cell 4 has one, a two-cell 5 has two — but a two-cell 10 has four. Scan the board for the extremes first and you buy certainty instead of options.
- Cash in the forced cages. That principle hands you the cages that can only be made one way. On a 9×9 board a two-cell 3 is 1+2, a two-cell 4 is 1+3, a two-cell 16 is 7+9, a two-cell 17 is 8+9; a three-cell 6 is 1+2+3, a three-cell 7 is 1+2+4, a three-cell 23 is 6+8+9, a three-cell 24 is 7+8+9. You may not know the order yet, but you know the digits — and if the whole cage sits inside one row, one column or one box, those digits are used up there, so strike them from every other cell in it. A cage that spills into a second box cannot be struck from either box that way — but if it still lies inside a single row or column, that house is fair game.
- Use the rule of 45. Every row, every column and every box on a 9×9 board contains 1 through 9, so it totals 45. Add up the cages that sit wholly inside one box: if they come to 38, the remaining cell in that box must be 7. On a 6×6 board the same trick works with 21.
- Extend it across a band. Three whole rows hold 1 to 9 three times over, so they total 135. Add every cage that lies wholly inside those three rows — say they come to 121. The band’s remaining cells, the ones belonging to cages that cross its edge, must therefore total 135 − 121 = 14. Any band works, not just the top one: for a middle band, cages cross both edges, and you still count only the cells inside. When just two cells are left over you are down to a handful of pairs — and because they sit in different cages, they may even be the same digit twice. On a 6×6 board, do the same with two rows and 42.
- Hand off between the sums and the sudoku. This is the join the whole puzzle turns on. Look at the close-up above: the 14 cage covers two cells, and one of them already shows a 9 — so its partner is 5, and that 5 is immediately unavailable to the rest of its row, column and box. Work in that rhythm. A cage narrows to two digits, ordinary sudoku decides which cell takes which, and the digit you place narrows the next cage.
- Pencil whole combinations, not single candidates. In killer it pays to note a cage’s possible digit sets in its corner. A three-cell cage of 9 gets “126 / 135 / 234” written in, because those are its only three options. Now suppose a 1 turns up elsewhere in a row that cage lies inside: the first two sets both need a 1 and both die, leaving 234 — the cage is solved without a single sum being added. That is why crossing off one combination often collapses a whole corner of the board: each set you kill takes digits out of play in three directions at once.
Sizes and Difficulty
The 9×9 board is the standard killer: nine digits, 3×3 boxes, and enough room for the long band arithmetic. The 6×6 board uses digits 1 to 6 with boxes two cells tall and three wide — a much shorter solve, and the friendlier introduction for younger solvers or a warm-up page.
Difficulty runs across seven graded levels — Very Easy, Easy, Normal, Hard, Very Hard, Tough and Extreme — and the grade describes the hardest technique the board actually requires, not how many clues it shows. The lower levels hand you starting digits; the upper levels are usually the classic cages-only form. New to killer? Start at Easy on a 6×6, then Normal on the 9×9. Very Hard upward is where the cages-only boards begin, and a solve becomes an evening rather than a coffee break. Teaching with these? The lower four levels are the ones where the arithmetic stays visible and every cage still has a foothold, so a class can work them inside a lesson.
Try It Online
Killer sudoku plays well in a browser: click a cell and type the digit you want, and clear it just as easily when a cage sum proves you wrong. The grid stays clean however many times you change your mind, which is worth a lot on a board where you are constantly testing one combination against another. Play a killer sudoku in your browser — no download, no sign-up. The general player controls — checking your answer, resetting, the timer, and working through a set — are covered once in How to Play Puzzles Online.
You Are Ready to Play
You now know what a killer sudoku is asking for, the rules that make every board solvable by logic alone, and a starting routine that works: read the extremes, cash the forced cages, use the rule of 45, then let ordinary sudoku finish the job. Ready to make your own? See How to Create Killer Sudoku Puzzles in Puzzle Maker Pro.
FAQ
Can a killer sudoku have more than one solution?
No. Every board is verified to have exactly one solution before it is printed, so any answer that satisfies all the rules is the answer.
Do you need to be good at maths to do killer sudoku?
No. Almost all of it is small sums and recognising which digit sets can make a total, which comes quickly with practice. The biggest arithmetic is the rule of 45 — and the band version of it at 135 — and each of those is a single subtraction.
What is the rule of 45 in killer sudoku?
Every row, column and box on a 9×9 board holds the digits 1 to 9, so it must total 45. Add the cages that sit entirely inside one of them, subtract from 45, and the difference is the total of the cells left over — often a single cell, which you can write straight in.
Can the same digit appear twice in one killer sudoku cage?
No. Digits never repeat inside a cage, even when the cage spans two boxes. That restriction is what makes a sum tell you something.
Why do some killer sudoku puzzles start with digits filled in?
The gentler difficulty levels fill in a few cells so there is an immediate foothold. The harder levels give you the cages alone — the classic form, where the arithmetic carries the whole puzzle.
Is killer sudoku harder than ordinary sudoku?
At the same graded level it asks about the same of you, but it asks differently: ordinary sudoku gives you digits and asks you to complete the grid, while killer sudoku gives you sums and asks you to work out the digits first. Every sudoku technique you already know still applies once the cages start yielding.