Killer Naked Single
A cell still has several Classic candidates, but its cage combinations leave exactly one of them. That surviving digit is a safe Naked Single.
What it is
Start with the ordinary row, column and box candidates. Then apply the sum, size and no-repeat rule of the cell’s cage. If the cage-compatible list shrinks to one digit while the Classic list was still longer, Killer arithmetic has turned a choice into a forced move.
How to spot it
Look for a short, restrictive cage near a cell with several pencil marks. A two-cell cage of 5, 6 or 17 is especially useful: its few legal pairs often leave only one digit that also respects the row, column and box.
Worked example
Step through the example. First the position, then the cage the argument rests on, then the candidates, and finally what follows from it.
Step 1 of 4: Starting position: the selected cell still has several ordinary Sudoku candidates.
- Pattern cells
- 4/1, 4/2
- Digits
- 4
- Follows from it
- 4/1
Press a marked square to point it out on the board above.
Why it matters
The digit must satisfy both layers at once. A normal candidate is not enough if it cannot belong to any valid cage combination; a cage digit is not enough if Sudoku already blocks it. The one digit surviving both checks is forced.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
Is this the same as an ordinary Naked Single?
The conclusion is the same, but the evidence is stronger: an ordinary Naked Single uses row, column and box only; this one also uses the cage sum and no-repeat rule.
Why not call it a cage combination?
A cage combination names the possible digit sets for a cage. This lesson makes the next move explicit: after intersecting that set with normal Sudoku candidates, one particular cell has only one digit left.
What should I check before placing the digit?
Check the candidate list from its row, column and box, then the cage’s legal combinations. If only one digit occurs in both lists, the placement is proven.
Put it to use
Where you will meet it
Medium grids are where this move starts to matter: the obvious cells run out and the pattern takes over.
Play MediumStuck on a grid of your own?
Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
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