Killer Sudoku

Sums instead of givens

The usual sudoku rules apply: 1 to 9 once in every row, every column and every 3×3 box. On top of that the grid is divided into dashed cages, each carrying a small number in its corner. The cells in a cage must add to that number, and no digit may repeat inside a cage.

A typical board here has about 33 cages of one to four cells, and only four or five digits printed anywhere. Almost everything comes from the sums.

The rule of 45

The technique that makes killer sudoku tractable, and the first thing to teach anyone starting.

Every row, column and box contains 1 to 9, so each adds to 45. Take a box whose cages sit entirely inside it: add their clues, and the difference from 45 is the total of whatever cells are left over. One cell left over means you have just solved it outright.

The same works across two or three rows — two rows total 90, three total 135 — and cages that spill across a boundary are handled by subtracting the part you can account for. Most opening moves in a killer sudoku are a version of this.

Cage combinations worth memorising

Small cages with extreme sums are fully determined, and they are where a board opens.

Two cells summing to 3 must be 1 and 2. Summing to 4, they are 1 and 3. Seventeen is 8 and 9; sixteen is 7 and 9. Three cells summing to 6 are 1, 2 and 3; summing to 24 they are 7, 8 and 9. Four cells summing to 10 are 1, 2, 3 and 4.

Mark both or all three candidates in the cells and let the row, column and box rules pick the order. That single habit carries you through the first third of a board.

No repeats in a cage, even across a box boundary

The rule people miss. A cage that straddles two boxes still cannot repeat a digit, even though the two cells are in different boxes and different rows and would otherwise be free to match.

It is also the rule that makes long cages informative rather than useless: a five-cell cage summing to 15 has to be 1+2+3+4+5, because no other five distinct digits are that small.

How these are built

A completed sudoku grid is generated first, then cages are laid over it and their sums computed. The result is checked against a solver: if the cage layout on its own pins the answer, the board ships with no givens at all, and if it does not, the smallest set of digits needed to make it unique is revealed. Nothing that has more than one answer is printed.

That is why the number of printed digits varies from board to board. Four or five is typical; a board that needed none is a good one.

Adjustments

Puzzles per page and the solutions page, plus a seed. A4 or US Letter.

One to a page is worth it here. Killer sudoku needs room in the cells for candidate digits, and the cage sums are printed small in the corners — two to a page is readable, four is a strain.

Print at 100% on A4 or US Letter.