What are innies and outies in Killer Sudoku?

Q: What are innies and outies in Killer Sudoku?

An innie is a cell inside a unit that belongs to a cage extending outside that unit. An outie is a cell outside the unit whose cage crosses into it. Using the 45 rule you can calculate the exact digit value of single-cell innies and outies.

Innies and outies are the specific cells you target when applying the 45 rule. Understanding them is the difference between getting stuck and finding free digits that unlock the rest of the puzzle.

Defining Innies and Outies

Consider a 3×3 box. Any cage with all its cells inside the box contributes fully to the box total. A cage with some cells inside and some outside is a crossing cage.

The cells of a crossing cage that sit inside the box are innies. The cells that sit outside the box are outies.

Using Innies

Sum all cage sums fully inside the unit. Subtract from 45. The result is the total of all innie cells. If there is only one innie, you have its exact value - Place it. If there are two innies summing to, say, 11, their candidates are restricted to pairs summing to 11: {2,9}, {3,8}, {4,7}, {5,6}.

Using Outies

Outies are handled symmetrically from the cage's perspective. A crossing cage has a known total. Subtract the values of the cells inside the unit (once known) from the cage total to find the sum of the cells outside - The outies. In the early game, outie logic becomes useful after innies have been partially resolved.

Practical Tips

Scan all 27 units (9 rows, 9 columns, 9 boxes) for 45-rule opportunities at the start of every puzzle.
Boxes tend to yield single-cell innies most often in Easy puzzles; harder puzzles require row and column applications.
On paper, circle crossing cage cells in a different colour to track which cells are innies vs full contributors.