If you already know classic Sudoku, Killer Sudoku adds a new layer of logic: numbered cages that tell you the sum of their cells. No digit repeats inside a cage, and every row, column and 3x3 box still must contain 1 to 9 exactly once. This post covers the basic rules and the first steps to solve a Killer puzzle without guessing.

What is Killer Sudoku?

Killer Sudoku uses the same 9x9 grid as standard Sudoku, but instead of (or in addition to) given digits, you see cages outlined with dashed lines. Each cage shows a small number, the sum of all digits inside that cage. For example, a 2-cell cage with a sum of 3 must contain the digits 1 and 2 in some order. A 2-cell cage with sum 4 must be 1 and 3. No digit repeats within a cage, and the digits in each row, column and 3x3 box must be 1 through 9 exactly once.

Because every row, column and box sums to 45 (the total of 1+2+…+9), you can use that fact to find missing digits, that is called the rule of 45. A well-made Killer Sudoku has exactly one solution and can be solved by logic alone.

Useful Fixed Cage Combinations

Some cage sums have only one possible combination of digits. Memorising these saves time. Here are the most common ones:

  • 2-cell cage of 3, must be 1 and 2
  • 2-cell cage of 4, must be 1 and 3
  • 2-cell cage of 16, must be 7 and 9
  • 2-cell cage of 17, must be 8 and 9
  • 3-cell cage of 6, must be 1, 2 and 3
  • 3-cell cage of 24, must be 7, 8 and 9

For other cage sums, there may be two or three possible sets. For instance, a 2-cell cage of 6 could be 1+5, 2+4, or (if the puzzle allows) 3+3, but remember that no digit repeats inside a cage, so 3+3 is not allowed. You will need to use the rest of the grid to narrow down which set works.

The Rule of 45

The rule of 45 is the most powerful tool in Killer Sudoku. Because each row, column and 3x3 box contains the digits 1 through 9 exactly once, the sum of all cells in that region is always 45. If you know the sum of all cages that lie entirely inside that region, subtract that from 45, and you get the value of the remaining cell (or the sum of the remaining cells).

How to Use the Rule of 45

Look for a row, column or box where all but one or two cells belong to cages that are completely inside that region. For example, suppose a row has four cages whose sums are 7, 11, 9 and 13, and all those cages lie entirely in that row. Add them: 7+11+9+13 = 40. Subtract from 45: 45-40 = 5. That means the one cell not in those cages must be 5. This works the same way with columns and boxes.

If a cage protrudes outside the region, you cannot use its full sum, you must consider only the part inside. But with practice, you will spot many opportunities to apply the rule of 45.

First Steps to Solve a Killer Sudoku

Start with the easiest deductions before moving to harder logic. Here is a practical order:

  1. List all cage combinations. For each cage, write down the possible digit sets that add to its sum. Use the fixed combinations above as a starting point.
  2. Apply the rule of 45. Scan rows, columns and boxes for cages that are fully inside. Subtract from 45 to find single cells or sums of remaining cells.
  3. Look for overlapping constraints. If a digit appears in only one possible combination for a cage, and that digit is already used in the same row, column or box, you can eliminate that combination.
  4. Use standard Sudoku logic. Once you have placed a few digits, treat the puzzle like a normal Sudoku: check rows, columns and boxes for missing numbers. The cages will often give you extra restrictions.
  5. Cross-check cage totals. If you have placed some digits in a cage, subtract their sum from the cage total to find what the remaining cells must add up to.

If you get stuck, go back to the rule of 45. It is surprisingly easy to miss a simple subtraction that reveals a single digit.

Where to Practice Killer Sudoku

You can find many free puzzles online, including daily challenges and different difficulty levels. One place that offers Killer Sudoku and more than 30 other variants is sudoku.by, where you can play online, track your progress and learn with technique guides.