How to Solve Killer Sudoku: 8 Proven Techniques

By Andrew Boyko, developer of CageDoku · Updated October 23, 2026

Killer Sudoku looks intimidating at first: there are no starting digits, only dotted cages with a small number in the corner. But every well-made Killer puzzle can be solved by pure logic, and most of the work is done by a handful of repeatable techniques. Here are eight of them, in the order you should reach for them.

Rules in 20 seconds

Fill the grid so every row, column and 3×3 box contains the digits 1 to 9 once. In addition, each dotted cage has a sum printed in its corner: the digits inside the cage must add up to that sum, and a digit cannot repeat inside the same cage. New to the game? Start with the Killer Sudoku rules or the beginner guide.

1. Memorise the cages with only one possible answer

Some cages can be built in only one way. A 2-cell cage with sum 17 must be 8 and 9. A 3-cell cage with sum 6 must be 1, 2 and 3; with sum 24 it must be 7, 8 and 9. A 4-cell cage with sum 10 is 1-2-3-4, and with sum 30 it is 6-7-8-9. You do not yet know which cell holds which digit, but you know exactly which digits may appear, so you can remove every other candidate. The full list is on the cage combinations chart.

2. Use the 45 rule

Every row, column and box adds up to 45. If the cages that sit completely inside a row, column or box cover all but one cell, that last cell equals 45 minus the sum of those cages. Example: in a box, the cages lying entirely inside it add up to 40 and cover eight of the nine cells. The ninth cell is 45 − 40 = 5, even though its own cage reaches outside the box. More in the 45 rule guide.

3. Look for innies and outies

Innies are cells of a region that belong to cages sticking out of it; outies are cells outside the region that belong to cages reaching into it. With exactly one innie, it equals 45 minus the cages completely inside. With exactly one outie, it equals the total of the cages you add minus 45. Example: two cages cover the whole top row plus one cell of the row below, and their sums total 52. That extra cell is 52 − 45 = 7. With two innies or two outies you cannot name them yet, but you know their sum, which is still a strong clue.

4. Cross out candidates with the combination list

Take a 3-cell cage with sum 8. The only digit sets are 1-2-5 and 1-3-4, so the cage always contains a 1 and can never contain 6, 7, 8 or 9. Remove those candidates from all three cells immediately.

5. Push must-have digits into the rest of the row, column or box

Stay with the same cage. If it lies entirely inside one row, then a 1 must be in the cage, so no other cell of that row can be 1. The same works for a column or a box. This is often the first elimination that cracks a puzzle open.

6. Use minimum and maximum bounds

A cage is limited by the digits it can still hold. A 4-cell cage with sum 28 cannot contain 1, 2 or 3: even if the other three cells are 9, 8 and 7 (24), the fourth must be at least 4. The same logic works from the other side for small sums.

7. Think in complements for big cages

For cages with five or more cells, think about which digits are missing. A 5-cell cage with sum 35 is 5-6-7-8-9; with sum 34 it is 4-6-7-8-9. A 7-cell cage with sum 40 leaves out two digits that add up to 45 − 40 = 5, so the missing pair is 1+4 or 2+3.

8. Do not forget classic Sudoku logic

Hidden singles, naked pairs and the rest still apply. After every placement, scan rows, columns and boxes, and use cage sums to finish cages: if a 3-cell cage has two known digits, the third is the sum minus those two.

A simple solving routine

1. Pencil in candidates from the cage combinations.
2. Apply the 45 rule to every row, column and box.
3. Look for innies and outies.
4. Place singles and update candidates.
5. Look for pairs and cage-line interactions, then repeat.

Practice makes it automatic

The fastest way to learn these techniques is to use them on real puzzles. CageDoku is a free, ad-free Killer Sudoku app (and browser version) whose hints name the exact technique and highlight the cells, so you learn the reasoning, not just the digit.

Frequently asked questions

Do I need to guess in Killer Sudoku?

No. A well-made puzzle can be solved by logic alone. In CageDoku every puzzle is solvable by human technique.

Can a digit repeat inside a cage?

No. Digits in a cage never repeat.

Which difficulty should I start with?

Start with Gentle and use hints; move to Moderate when the 45 rule feels natural.

How is Killer Sudoku different from classic Sudoku?

Classic gives you starting digits; Killer gives you cage sums, so arithmetic replaces the givens.

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