How to Solve Killer Sudoku: Where to Start

How to start a Killer Sudoku: the 24 cages that can be filled only one way, the 45 rule worked through on one box, and how to narrow down the rest.

Updated 2026-11-05

The rules in one minute

Killer Sudoku is a 9×9 Sudoku that usually starts with no digits at all. Instead, dashed outlines called cages group the squares, and each cage shows the sum of its digits. Fill the grid so that every row, column and 3×3 box holds 1 to 9 once, every cage adds up to its sum, and no digit repeats inside a cage.

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Step 1: the cages with only one way

Some sums leave no choice. Two squares that add up to 3 can only be 1 and 2; three squares that add up to 24 can only be 7, 8 and 9. For every cage size from 2 to 7 squares there are exactly four such sums: the two smallest and the two largest. These 24 cages are where to begin, because you know their digits at once and only have to work out the order.

Squares	Sum	Digits
2	3	1 + 2
2	4	1 + 3
2	16	7 + 9
2	17	8 + 9
3	6	1 + 2 + 3
3	7	1 + 2 + 4
3	23	6 + 8 + 9
3	24	7 + 8 + 9
4	10	1 + 2 + 3 + 4
4	11	1 + 2 + 3 + 5
4	29	5 + 7 + 8 + 9
4	30	6 + 7 + 8 + 9
5	15	1 + 2 + 3 + 4 + 5
5	16	1 + 2 + 3 + 4 + 6
5	34	4 + 6 + 7 + 8 + 9
5	35	5 + 6 + 7 + 8 + 9
6	21	1 + 2 + 3 + 4 + 5 + 6
6	22	1 + 2 + 3 + 4 + 5 + 7
6	38	3 + 5 + 6 + 7 + 8 + 9
6	39	4 + 5 + 6 + 7 + 8 + 9
7	28	1 + 2 + 3 + 4 + 5 + 6 + 7
7	29	1 + 2 + 3 + 4 + 5 + 6 + 8
7	41	2 + 4 + 5 + 6 + 7 + 8 + 9
7	42	3 + 4 + 5 + 6 + 7 + 8 + 9

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Step 2: the 45 rule

Each row, column and box holds 1 to 9 once, so it always adds up to 45. When some cages lie completely inside a box, add up their sums: what is missing from 45 is the total of the box's other squares.

In the box below, three cages lie completely inside it, with sums 14, 9 and 18: 41 in all. The shaded square belongs to a cage that runs on into the next box, so it is the only square left, and it must be ⁦45 − 41 = 4⁩.

One 3×3 box with three cages inside it. The shaded square is ⁦45 − 41 = 4⁩.

Step 3: narrow down the rest

Most cages can be filled in more than one way. Keep only the ways that still fit the digits around them.

A two-square cage of 10 can be 1 and 9, 2 and 8, 3 and 7 or 4 and 6, but never 5, because 5 and 5 would repeat a digit.
If a digit is in every combination that is still possible, the cage must contain it.
If such a cage lies within one row, column or box, that digit cannot go anywhere else in that row, column or box.
Use the 45 rule on rows and columns too, and on two or three boxes together.
Write a cage's possible digits as small notes, then place them as in a classic Sudoku.

Sudoku variants: Killer, Jigsaw, Diagonal, Samurai and more →

Practice

Every Find the Mistake puzzle on this site has exactly one wrong digit, and you can play each board right on its page.

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