Killer Sudoku & Kakuro Combinations Calculator

How to use the calculator and the tables

A Killer Sudoku cage and a Kakuro run follow the same rule: a fixed number of cells, different digits from 1 to 9, and a given sum. That is why one table serves both games. Choose the number of cells and the sum, and the calculator lists every set of digits that fits.

• Cells and sum. Pick how many cells the cage or run has and what it adds up to. Only sums that are possible for that cell count are offered.
• Must include. Tick digits you already know are in the cage. The list keeps only the sets that contain all of them.
• Must not include. Tick digits that cannot be used, for example because they are already in the same row of a Killer Sudoku. The list drops every set that contains them.
• Digits that always appear. When several sets remain, the note under the list names the digits they all share. Those digits are certain to be in the cage, even if you do not yet know where.

The complete tables above are plain text. Each row gives a sum, how many sets reach it and the sets themselves. Rows with a single set are in bold: those are the combinations worth memorising, because they let you fill candidates without any arithmetic.

Using the table in Killer Sudoku

In Killer Sudoku, look up the cage's cell count and sum, then cross out sets that contain a digit already placed in the cage's row, column or box. The 45 rule often tells you one cell of a cage by itself; the table then tells you what the other cells can be.

Using the table in Kakuro

In Kakuro, every run has a clue, and runs cross each other. Look up both runs of a cell and keep only the digits that appear in a set of each. When the two lists share a single digit, that cell is solved.

FAQ

How many combinations are there in total?

For 2 to 9 different digits from 1 to 9 there are 502 combinations across all sums. Most sums can be made several ways, and only a few have exactly one.

Is a sum of 45 possible with fewer than nine cells?

No. Nine different digits are needed to reach 45, so 45 appears only in the nine-cell table.

Why do some cell counts have a single combination at both ends of the table?

The smallest and largest sums for a cell count can each be made only one way: the lowest digits together, or the highest digits together. For three cells that is 1+2+3 = 6 and 7+8+9 = 24.

Can a digit repeat in a Kakuro run?

No. As in a Killer Sudoku cage, the digits of a Kakuro run must all be different, which is what makes these tables valid for both games.