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Killer sudoku rules in full
The ordinary Sudoku rules still apply: each row, column and 3 by 3 box holds 1 to 9 once each. On top of that come the cages, groups of squares marked with a dotted line or a shade of colour, with a total in one corner.
- The numbers in a cage add up to its total.
- No number appears twice in a cage, even when the cage bends across two boxes.
- A cage can be anything from two squares to nine.
The puzzle is usually credited to the Tokyo puzzle setter Tetsuya Nishio, and it first appeared outside Japan in The Times in 2005. Because the grid starts almost empty, the first moves come from arithmetic rather than scanning for a missing number.
Killer sudoku combinations worth learning first
Most cage totals can be made several ways: 10 in two squares could be 1 and 9, 2 and 8, 3 and 7 or 4 and 6. The useful cages are at the very low or very high end, where only one set of numbers fits:
| Cage size | Total | Only possible numbers |
|---|---|---|
| 2 squares | 3 | 1, 2 |
| 2 squares | 4 | 1, 3 |
| 2 squares | 16 | 7, 9 |
| 2 squares | 17 | 8, 9 |
| 3 squares | 6 | 1, 2, 3 |
| 3 squares | 7 | 1, 2, 4 |
| 3 squares | 23 | 6, 8, 9 |
| 3 squares | 24 | 7, 8, 9 |
| 4 squares | 10 | 1, 2, 3, 4 |
| 4 squares | 11 | 1, 2, 3, 5 |
| 4 squares | 29 | 5, 7, 8, 9 |
| 4 squares | 30 | 6, 7, 8, 9 |
You will not know which way round they go yet, but you can pencil them in and rule out everything else. Nearly unique cages help too. A total of 5 in two squares is 1 and 4 or 2 and 3, so 5 to 9 are out. A total of 15 in two squares is 6 and 9 or 7 and 8, so nothing below 6 fits. An eight square cage is simply 1 to 9 with one number missing, and the missing number is 45 minus the total.
The 45 rule: innies and outies
Add 1 to 9 together and you get 45, so every row, column and box in a finished grid adds up to 45. This is the most useful idea in the puzzle.
Innie. Suppose the cages lying wholly inside a row add up to 38, and one square of the row belongs to a cage that pokes out of it. That square is the innie, and it must be 45 minus 38, which is 7.
Outie. Now suppose a set of cages covers a whole box plus one extra square that pokes outside it, and those cages add up to 52. The extra square is the outie, and it must be 52 minus 45, which is 7.
The rule scales up: two rows, columns or boxes add up to 90, three to 135, and so on. It also works with more than one leftover square. If the cages wholly inside a box add up to 40, the two squares left over must add up to 5, even if they sit in different cages. That makes a pretend cage of 5 in two squares: 1 and 4 or 2 and 3.
Tips for getting started
- Mark the unique cages first. Pencil in every cage from the table above.
- Sweep for innies and outies. Check every box, row and column early, and again whenever you get stuck.
- Let cages act like Sudoku pairs. If a two square cage of 3 sits wholly in one row, those squares hold the 1 and the 2, so no other square in that row can be 1 or 2.
- Find the numbers every option shares. Four squares adding up to 28 are either 4, 7, 8 and 9 or 5, 6, 8 and 9. Either way, 8 and 9 are in there, and 1 to 3 are not.
- Switch to normal Sudoku when the cages run dry. Our guide to Sudoku techniques from beginner to expert covers pairs, pointing and X-Wings, and they all work here too.
Questions people ask
Can a number repeat in a killer sudoku cage?
No. Each number appears once per cage, as well as once per row, column and box. Some early puzzles did not spell this out, but it is standard now.
What is the 45 rule?
Every row, column and box holds 1 to 9 once, so each adds up to 45. If you know the totals of all but one square in a row, column or box, that square is 45 minus the rest.
Do I need to learn every cage combination?
No. The unique ones above do most of the work. For anything else, write out the possible sets and see which numbers they share or rule out.
Where Thinking Cap helps, and where it does not
Thinking Cap: Sudoku & Logic is our Sudoku and logic puzzle game for Android. Killer is one of three Sudoku variants in it, alongside Jigsaw and Thermo. Thinking Cap only keeps a puzzle if its own step by step solver can finish it.
Stuck? Tap Hint and the tutor nudges you towards the right part of the grid. Tap it again and it highlights the pattern and explains why the step works.
Today’s Sudoku is free every day, and on Sundays it is a variant. Killer, Jigsaw and Thermo take turns, so Killer comes round one Sunday in three. Thinking Cap Pro lets you play all three variants whenever you like, at Moderate, Tricky and Tough, with either a yearly Puzzle Pass or a one-time Lifetime payment. The Google Play listing has the full details of what is free and what is in Pro.
What it will not do: check a Sudoku from a newspaper or book, as it only works with the Sudoku it makes itself. It is Android only, and out now on Google Play.
Sources
- Killer sudokuWikipedia en.wikipedia.org
- Andrew Stuart, The Daily Killer Sudoku and how to playSudokuWiki.org sudokuwiki.org
- Andrew Stuart, Killer CombinationsSudokuWiki.org sudokuwiki.org
- Andrew Stuart, Innies and OutiesSudokuWiki.org sudokuwiki.org
- Thinking Cap: Sudoku & LogicGoogle Play play.google.com