Killer SudokuSums of dotted cages as clues: free to play and print

1Killer Sudoku rules

Every column, every row and every bold 3×3 box holds each digit 1 to 9 once. So far it is the same as classic sudoku.

The number at the top left of a dotted group of cells (a cage) is the sum of the digits inside it. A digit cannot repeat within a cage.

How it differs from classic sudoku

Clues

Dotted cage sums, in place of starting digits

Clues

A few at Easy only (about 8). 0 from Medium up

Rules

Besides columns, rows and boxes, a digit cannot repeat within a cage

Level

5: Easy, Medium, Hard, Oni and Master

Solving order

With a new puzzle, look in this order. Whenever a digit is placed, start again from the top.

1. Sums with only one combination: With 2 cells, sums like 3, 4, 16 and 17, and with 3 cells, sums like 6, 7, 23 and 24, have fixed digits (see the table below).
2. Digits a 2-cell sum cannot use: A digit cannot repeat, so with 2 cells a sum of 10 cannot use 5. With an even sum, the digit that is exactly half of it is out.
3. Rule of 45: Subtract the sums of the cages that fit wholly inside a row, column or box from 45 to get the sum of the remaining cells.
4. Narrow down the combinations: Remove digits already used in the same row, column or box from a cage's combinations.
5. Classic sudoku techniques: once digits start going in, you can also use classic sudoku techniques (hidden singles and so on) as they are.

See how to solve it, step by step

Step through real boards one move at a time.

Expert techniques

At Oni and Master, and at the levels other apps call "Expert", you need the ideas below.

• The Rule of 45 across several rows or columns: 2 rows total 90, and 3 rows (3 boxes side by side) total 135. Even when a single row is no use, taking several together can make cages fit wholly inside. For one row, see it step by step.
• Compare the cells sticking out with the cells reaching in: You can sometimes work out the difference between the cells sticking out of a box and the cells reaching into it (for example, the 1 cells sticking out are 3 greater than the 1 cells reaching in). Knowing the difference narrows down the digits.
• Upper and lower limits of a sum: A cage's sum can only fall within a certain range.

• 2 cells 3–17
• 3 cells 6–24
• 4 cells 10–30
• 5 cells 15–35

For example, 3 cells summing to 7 can only be 1, 2 and 4 (the closer to the minimum of 6, the smaller the digits).

Sums with only one combination

These sums have only one combination. When you find one, the digits in that cage are settled.

Combination table (2 to 4 cells)

Every combination for each sum in cages of 2 to 4 cells. "Always in" lists digits in every combination. "Never in" lists digits in none. Sums with just one combination are coloured.

For cages of 5 or more cells, think about the digits they do not use. For n cells summing to s, the 9−n unused digits total 45−s. For example, 6 cells summing to 38 leave 3 unused digits totalling 7, so the table above shows that 1, 2 and 4 are not used.