Killer Sudoku
Killer Pair
A Killer Pair is a naked pair created by a cage. Work out every way the cage can still be filled; if two of its cells sit in the same row, column or box and, in every one of those ways, they use the same two digits, then those two digits belong to that pair. Every other cell of that house loses them — even when the two cells' pencil marks list more than two candidates.
What you need to see on the grid
Look for a Killer Pair when a cage has only a few ways left to make its sum, and two of its cells share a row, column or box. Four terms carry the method:
- Valid fills
- The ways to give each empty cell of the cage one of its candidates, all different, so the cage reaches its sum.
- The pair
- Two cells of the cage in one house whose values, across all valid fills, are always the same two digits.
- The house
- The row, column or box both cells share. Its other cells lose the pair's digits, exactly as with a naked pair.
- The pointing form
- A close cousin the app also calls Killer Pair: a digit every valid fill uses, always in cells of one house. It leaves that house outside the cage.
How to apply it, step by step
One example runs through all four steps, late in an expert Killer puzzle from the app, at the exact point where its hint needs a Killer Pair. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them. The dashed outline is the cage, its sum in the corner.
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Step 1Work out the ways the cage can still be filled
Take a cage with few empty cells and list how it can still reach its sum. The 24-cage covers R2C6, R2C7, R3C6 and R3C7. R2C7 and R3C7 can only be 6 or 9, and two cells of one cage never repeat a digit, so between them they hold 6 and 9: 15.
That leaves 24 − 15 = 9 for R2C6 and R3C6. R2C6 is 2 or 7, R3C6 is 1, 2 or 7: the only ways to make 9 are 2 + 7 and 7 + 2.
The 24-cage alone. R2C7 + R3C7 = 6 + 9, so R2C6 + R3C6 = 9 = 2 + 7. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 24 R3 R4 R5 R6 R7 R8 R9 - Cage cell in column 6: always 2 or 7
- Candidates 2 and 7, the digits studied
- Cage, sum in its corner
- Not needed for this step
Filled in: the cage. The other 77 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 2Find cage cells in one house that always take the same digits
R2C6 and R3C6 are both in column 6, and every fill of the cage puts 2 in one of them and 7 in the other. So column 6's 2 and 7 are both inside this pair, even though R3C6 still lists a 1 as well.
That is the Killer Pair: a naked pair that the pencil marks alone do not show, made visible by the cage sum.
Column 6 and the cage. R2C6 and R3C6 are always 2 and 7, in some order. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 24 R3 R4 8 R5 4 R6 5 R7 9 R8 6 R9 3 - Digit already on the grid
- Column 6
- Cage cell in column 6: always 2 or 7
- Candidates 2 and 7, the digits studied
- Cage, sum in its corner
- Not needed for this step
Filled in: column 6; the cage. The other 70 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 3Remove those digits from the rest of the house
Column 6 holds 2 and 7 once each, and both are taken by R2C6 and R3C6. Every other cell of the column loses 2 and 7: here only R1C6 is still open, and it loses both.
The rest of the cage is not touched: R3C6 keeps its 1 for now, because only the cage arithmetic, not the column, rules it out.
Technique: Killer Pair
R1C6, the only other open cell of column 6, loses 2 and 7. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 24 R3 R4 8 R5 4 R6 5 R7 9 R8 6 R9 3 - Digit already on the grid
- Column 6
- Cage cell in column 6: always 2 or 7
- Candidates 2 and 7, the digits studied
- Candidate removed
- Cage, sum in its corner
- Not needed for this step
Filled in: column 6; the cage. The other 70 cells are left blank: they are not needed for this step. Removed: 2 from R1C6; 7 from R1C6.
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Step 4Collect what the elimination unlocks
R1C6 had three candidates, 1, 2 and 7. With 2 and 7 gone, only 1 is left: a Naked Single, and the app's next hint in this puzzle.
Technique: Naked Single
Row 1 after the Killer Pair. R1C6 has only 1 left. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 3 6 5 8 9 1 4 R2 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- The cell that must be 1
- Candidate 1, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 1. The other 72 cells are left blank: they are not needed for this step. Placed: R1C6 = 1.
Common mistakes
Missing a valid fill
The pair is only locked if it holds in every way the cage can be filled. Forget one combination — a 1 + 8 here, if R2C6 could be 8 — and the pair may hold a digit you did not count. List the fills from the candidates, not from memory.
Cells that do not share a house
The digits leave only the house both cells share. R2C6 and R3C6 share column 6 and box 2; a cell that sees just one of them — R2C1, say — can still hold the digit the other one takes.
Clearing the cage's own cells
R2C7 and R3C7 are in the cage but not in column 6; they are not part of the pair's house, and the step says nothing about them. Only the other cells of the house lose the pair's digits.
Keep going
- Cage CombinationsList a cage's combinations, cross them with the grid, and clear every candidate no surviving combination can use.
- Naked PairTwo cells locked to the same two digits clear those digits from every unit they share.
Every cage combination, for every size and sum: Killer Sudoku Cage Sum Chart — all combinations
Learn the move, not just the digit
In a real game, when a Killer Pair is what opens the next cell, the hint in the app names it and shows the cell it unlocks — the same move as step 4 above.