How to Solve Killer Sudoku: Beginner Strategies Step by Step

Learning how to solve a Killer Sudoku is mostly learning where to look first. The grid has no starting digits, only dotted cages with a sum, so the first move always comes from arithmetic and never from a digit you can see. This guide gives you the order of attack that works on every grid, then plays the first moves of a real puzzle with exact cell references.

Read the grid before you write

A Killer Sudoku follows the rules of classic Sudoku: each row, column and 3 x 3 box holds 1 to 9 once. On top of that, the grid is cut into cages drawn with dotted lines. The small number in the corner of a cage is the sum of its digits, and a digit never repeats inside a cage.

Before you write anything, scan the whole grid three times. First, count the cages of one cell: they are free digits. Second, look at the cages of two and three cells with an extreme sum, very small or very large. Third, check the boxes, rows and columns for the rule of 45 described below. Only then pick up your pencil.

In this article a cell is named by its row (counted from the top) and its column (counted from the left), so R2C4 is the cell in the second row and fourth column.

The sums that have only one answer

Because digits cannot repeat in a cage, some sums can be made in just one way. Learn this short list and a large part of the early game becomes automatic. We computed it with a script that tries every set of different digits.

These cages do not tell you the order of the digits, only which digits are inside. That is still a lot: a cage of 3 cells with a sum of 24 holds 7, 8 and 9, so none of those digits can appear again in its row, column or box outside the cage.

The rule of 45

Every row, every column and every box adds up to 1 + 2 + ... + 9 = 45. When some cages sit completely inside a box, add their sums and subtract the total from 45. What remains is the sum of the cells of the box that are not inside those cages. If only one cell is left, you have found its digit without any guess. This is the most powerful tool of the game, and the one beginners forget.

The first moves of a real grid

This is an easy Killer Sudoku from the LogikLand generator (cages of up to 3 cells), with its solution. We checked each move below against the real grid with a script.

1. Cages of one cell. R2C2 shows 8, R7C1 shows 1 and R9C1 shows 9. Write them in.
2. Sums with one answer. The two-cell cage at R1C5 and R2C5 has a sum of 3, so it holds 1 and 2. The three-cell cage on the top row (R1C6 to R1C8) has a sum of 24, so it holds 7, 8 and 9.
3. The rule of 45 on the middle box. Three cages sit entirely inside the central box: the vertical cage of 19 in column 4, the vertical cage of 11 in column 6, and the cage of 9 made of R5C5, R6C5 and R6C6. They add up to 19 + 11 + 9 = 39. The box has 45, so the one cell left, R4C5, is 45 - 39 = 6.
4. Use the cage that spills out. R4C5 belongs to a two-cell cage of 13 that also contains R3C5. So R3C5 = 13 - 6 = 7.
5. The rule of 45 on the bottom right box. The cages of 19, 13 and 10 sit inside it. They add up to 42, so R7C9 = 45 - 42 = 3. That cell belongs to a cage of 9 with R6C8 and R6C9, which must therefore add up to 6.

From here, column 5 holds 1 and 2 at the top, then 7 and 6, which blocks those digits elsewhere in the column, and the small cages start to fall one after the other.

Pencil marks and order of work

Once the first digits are in, switch to pencil marks. In each cell write the digits still possible, using three filters: the digits of its row, column and box that are already placed, the digits that its cage can still use, and the combinations left for the sum.

A good order

• Finish the cages of one cell and the single-answer sums.
• Apply the rule of 45 to all nine boxes, all rows and all columns.
• For a two-cell cage, list its pairs and cross out those that use a digit already in the row, column or box.
• When a digit has only one possible place in a row, column or box, write it, as in classic Sudoku.

Common mistakes

• Repeating a digit inside a cage. A cage is a small row: its digits are all different.
• Forgetting that the sum is for the whole cage, including cells in different rows or boxes.
• Adding the cages of a box when one of them is only partly inside it. Only cages entirely inside the unit count for the rule of 45.
• Guessing early. A guess in a Killer Sudoku is hard to undo because every cage is linked to others.

The four levels of the LogikLand Killer assistant change the size of the cages: up to 3 cells at the easy level, 4 at medium, 5 at hard and 6 at expert, with fewer cages at the top level. Bigger cages mean fewer exact sums, so the single-answer table helps less and the rule of 45 matters more. When you are ready for those, read advanced Killer Sudoku techniques. If you are new to the game, start with the Killer Sudoku rules.

Questions