How to Solve Killer Sudoku

Killer Sudoku crosses a normal grid with a small sums puzzle. The three classic rules still apply, but the starting numbers are usually gone — the clues are cage totals instead. Here is how to read them.

The rules, quickly

Every row, column and 3×3 box still holds 1 to 9 exactly once. On top of that, the board is carved into dashed cages, each printed with a target total, and a digit may not repeat inside a cage even where the row, column or box would allow it. Most boards begin with no given numbers at all, so the cage totals carry the whole puzzle.

Cage combinations worth knowing

Because a cage cannot repeat a digit, small cages with extreme totals often have just one possible set of numbers. These become your first footholds:

Two cells: 3 is {1,2}; 4 is {1,3}; 16 is {7,9}; 17 is {8,9}.
Three cells: 6 is {1,2,3}; 7 is {1,2,4}; 23 is {6,8,9}; 24 is {7,8,9}.
Four cells: 10 is {1,2,3,4}; 30 is {6,7,8,9}.

You do not need to memorise them all. Simply noticing that a small cage with a very high or very low total is tightly constrained tells you where the puzzle opens first.

The rule of 45

Every row, column and box contains 1 through 9, which always sum to 45. That fact is the key that plain Sudoku logic cannot see. If cages fill a box except for one stray cell, subtract the cage totals from 45 and you have that cell exactly. The same trick — often called innies and outies — works across rows and columns, and it repeatedly cracks boards that look impossible.

Putting it together

Start with the tightly constrained cages to place a few certainties, use the rule of 45 to pin down stray cells, then let ordinary Sudoku technique take over: each number you place tightens both its unit and its cage. Pencil notes are essential here for tracking which combinations survive.

A sample deduction from start to finish

Picture a three-cell cage totalling 7 sitting in the top row, next to a two-cell cage totalling 4. The three-cell 7 can only be {1,2,4}, and the two-cell 4 can only be {1,3}. Notice that both cages want a 1, but they share the same row — so the 1 cannot live in both. That single observation often forces the 1 into one specific cage, which in turn fixes the other numbers around it. This is the rhythm of Killer Sudoku: you rarely place a number because a cell demands it, but because a combination somewhere else has quietly run out of alternatives. One cage constrains the next, and the grid unravels a lobe at a time.

Mistakes that trip up newcomers

Two habits slow most people down when they first meet cages. The first is forgetting the no-repeat rule inside a cage: a four-cell cage of 12 cannot be 3+3+3+3, because a digit may not repeat within the cage, even though 3+3+3+3 sums correctly. The second is treating cages in isolation. A cage total is only half the information; the other half is the row, column and box each of its cells also belongs to. The strongest deductions almost always come from combining a cage's possible sets with what its cells' units already forbid. Hold both constraints in mind at once and cages that looked impossible suddenly have a single answer.

Build up gradually

Killer Sudoku rewards patience more than raw speed, so there is no shame in starting on the easier boards, where larger cages and gentler totals give more away. As you grow comfortable spotting the tight two- and three-cell cages and applying the rule of 45, the harder grids stop feeling like arithmetic and start feeling like the same clean logic you already know, just approached from a new direction.

Ready to try it? Play Killer Sudoku now, and if you want to sharpen the underlying logic first, warm up on the classic grid at Sudoku AZ or push yourself with Expert Sudoku.