Killer Sudoku solving techniques

Cage combinationstier 1

When: A cage sum in so many cells can only be made a few ways; its cells take digits from those ways.

List the ways a cage can add up to its sum with distinct digits and the candidates its cells have left. A cell keeps only the digits that appear in some way that works.

From one of our puzzles (6x6): The cage of 17 in 4 cells (A1, B1, C1, D1) can only be 2+4+5+6 with the candidates left, so A1, B1, C1, D1 lose the other digits.

Practise it: Killer Sudoku puzzles at Easy

Naked singletier 1

When: A cell with one possible digit takes it; the digit leaves its row, column, box and cage.

A cell with one candidate takes that digit; it then leaves every other cell of the row, column, box and cage.

From one of our puzzles (6x6): D1 can only be 5, so 5 is ruled out for the other cells of its row, column, box and cage.

Practise it: Killer Sudoku puzzles at Easy

Hidden singletier 1

When: A digit with only one possible cell in a row, column or box goes there.

If a digit can go in only one cell of a row, column or box, it goes there, whatever else that cell could hold.

From one of our puzzles (6x6): In box 2, only D1 can take 5.

Practise it: Killer Sudoku puzzles at Easy

Rule of 45tier 2

When: A row, column or box adds up to 45; subtract the cages inside it to get the sum of the cells that stick out or in.

A house holds 1 to 9, total 45. Subtract the cages wholly inside it; the rest is the sum of the cells not covered (the innies), or of the cells of overlapping cages that stick out (the outies). Treat them like a new small cage.

From one of our puzzles (9x9): Row 1 adds up to 45; the cages wholly inside make 15, so A1, B1, C1, I1 add up to 30 (6+7+8+9). A1, B1, C1, I1 lose the rest.

Practise it: Killer Sudoku puzzles at Medium

Naked pairtier 2

When: Two cells of a house with the same two candidates own those digits; the rest of the house loses them.

Two cells of a house that can only hold the same two digits keep them; the rest of the house loses those digits.

From one of our puzzles (9x9): G1, G2 in column G can only hold 2, 4 between them, so the other cells of column G cannot.

Practise it: Killer Sudoku puzzles at Hard

Cage inside a housetier 2

When: A digit a cage must contain, with all its places in one house, leaves the rest of that house.

If a cage must contain a 9 and all its places for the 9 lie in one row, column or box, no other cell of that house can be 9.

From one of our puzzles (9x9): The cage of 18 at D1, E1, F1 must contain a 8, and every place it can go is in row 1, so no other cell of row 1 is 8.

Practise it: Killer Sudoku puzzles at Hard

Rule of 45 on several housestier 3

When: Two or three neighbouring rows, columns or boxes add up to 90 or 135; the same subtraction works.

The rule of 45 also works on two or three neighbouring rows, columns or boxes: 90 or 135 instead of 45. The bigger area catches cages that one house cannot.

From one of our puzzles (9x9): The cages that touch row 8 and row 9 add up to 116, 26 more than row 8 and row 9 hold, so the cells sticking out, H6, C7, E7, F7, G7, H7, add up to 26 (2+3+4+5+6, 1+2+4+6+7, 1+2+3+4+8, 1+2+3+6+8 and 2 more). C7 loses the rest.

Practise it: Killer Sudoku puzzles at Hard

Hidden pairtier 3

When: Two digits that fit only the same two cells of a house fill them; those cells lose other candidates.

Two digits that fit only the same two cells of a house fill those two cells; their other candidates go.

From one of our puzzles (9x9): In column H, 1 and 7 fit only H5, H6, so those two cells hold nothing else.

Naked tripletier 3

When: Three cells of a house sharing three candidates own those digits.

Three cells of a house that share three candidates between them own those three digits.

From one of our puzzles (9x9): A3, F3, G3 in row 3 can only hold 1, 2, 5 between them, so the other cells of row 3 cannot.

Contradictiontier 4

When: If a digit in a cell leads to a broken rule a few steps later, that digit is out.

Assume a digit, follow every technique above, and look for a broken cage or a repeated digit. If one appears, the digit is out. This is what makes an Expert killer Expert.

From one of our puzzles (9x9): Suppose I1 were 8: following the rules from there, the cage of 26 at F1 cannot be completed. So I1 is not 8.

Practise it: Killer Sudoku puzzles at Expert