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## Cage Unit OverlapFrom sudokuwiki.org, the puzzle solver's site |

This is an important Killer Sudoku strategy which I have placed at the start of all the more complex strategies in the solver because it is so useful and very easy to spot. It is related to Intersection Removal. Whereas IR is the overlap of rows/columns with boxes, this is the overlap of 'cages' with rows, columns and boxes.

Each 'cage' is made up of one or more 'combinations' - sets of numbers that total the cage clue. If you can find a candidate number inside that cage that is not found elsewhere on the row, columns or box the cage is aligned on, then you know that number must appear in the cage. That part is self-evident since, in the solver at least, these numbers are displayed. Given that number is true, we can remove all combinations which omit that number. Often that means we can remove a bunch of numbers.

Each 'cage' is made up of one or more 'combinations' - sets of numbers that total the cage clue. If you can find a candidate number inside that cage that is not found elsewhere on the row, columns or box the cage is aligned on, then you know that number must appear in the cage. That part is self-evident since, in the solver at least, these numbers are displayed. Given that number is true, we can remove all combinations which omit that number. Often that means we can remove a bunch of numbers.

In the first example below, two such

The blue ringed cage, a 3-cell with a clue of 19 gives us five different combinations. But the 9 in that cage is unique to both the cage and row H, so only the combinations with 9 in them are valid. {4,7,8} and {5,6,8} are not possible. Of the remaining candidates, the 5s can be removed.

In this second example, five

I'll leave it to you to show how the other four cages have similar eliminations.

Overall, most Killer Sudoku puzzles will have at least one example of this strategy so they are well worth looking out for, and often you can reduce the puzzle with this method while looking into the cages with multiple combinations. Keep an eye out on the rows, columns and boxes you are studying.