Cage subsets (Rule of K)
Cage arithmetic restricts a triple or quad to exactly K digits; those digits are then locked in one row, column or box.
What it is
Several cells share a Sudoku unit. Their cage-compatible candidates combine to exactly as many digits as cells.
How to spot it
Look for three or four marked cells whose sums and candidates reduce them to the same small digit pool.
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: Two 5-cages lie entirely in row 6.
- Pattern cells
- 6/4, 6/5, 6/6, 6/7
- Digits
- 1, 2, 3, 4
- Follows from it
- 6/1, 6/3, 6/8, 6/9
Press a marked square to point it out on the board above.
Why it matters
Those K digits must occupy those K cells in some order, so they cannot occur elsewhere in that unit.
Practise now
The practice puzzle is picked so that this technique is what gets the solve moving again.
Frequently asked questions
Why is this different from a naked subset?
The conclusion is identical, but the cage sums create or sharpen the candidate pool before the unit locks it.
Can K be two?
Yes; that is the earlier Killer Pair. This lesson focuses on the more demanding triples and quads.
Where do eliminations happen?
Only in the same row, column or box as the locked cells—not automatically throughout their cages.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
Play ExpertStuck 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.
Open the solverFinished reading? Mark it done and the learning path remembers where you got to.