Cage/Unit Overlap
Cage/Unit Overlap is a Killer Sudoku technique that borrows the logic of pointing pairs and applies it to cages. Importantly, it's a candidate-elimination technique, not a sum technique — it works on where digits can go, not on arithmetic totals.
How it works
Wherever a cage and a unit (row, column or box) share some cells, that overlap can be used two ways:
- Cage into unit. If a candidate for the cage is confined to the cells it shares with a unit, then the cage will place that digit inside the overlap — so the digit can be removed from the rest of the unit.
- Unit into cage. If a digit can only go, within a unit, in the cells that unit shares with a cage, then that digit is claimed for the overlap — so it can be removed from the rest of the cage.
Either way you're using the fact that a digit locked to the shared cells must be placed there, exactly like a locked candidate — just with a cage playing the role of one of the regions.
A cage (green, dashed — it continues above the box) shares two cells with this box. If the cage can only place its 3 in those two shared cells, the 3 is claimed for the overlap, so it is eliminated from the rest of the box (✗3). No sums involved — pure candidate elimination.
Step by step
- Find a cage overlapping a unit in two or more cells.
- Check a digit's candidates. Are they confined to the overlap, from the cage's side or the unit's side?
- Eliminate the digit from the rest of whichever region doesn't own the overlap.
Why it's distinct from innies/outies
It's easy to lump all Killer techniques together as "sum tricks", but cage/unit overlap is different: it never adds anything up. It's pure intersection logic — the Killer cousin of pointing pairs and box/line reduction. Pair it with the arithmetic techniques (the rule of 45, combinations) and you have both halves of Killer solving.
Common mistakes
- Treating it as a sum. This is candidate elimination — don't go looking for totals.
- Clearing the wrong region. A digit locked to the overlap clears the rest of the other region, not the overlap itself.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.