Innies and outies

An innie is a cell that sits inside a house but belongs to a cage that mostly lives outside it. An outie is the opposite: a cell that sits outside the house but belongs to a cage that mostly lives inside. They are the loose ends of the 45 rule, and intermediate killer sudoku is full of them.

Suppose a box contains three complete cages summing to 28, and two cells of a fourth cage. Those two cells are innies. The box must total 45, so the innies add to 17. Two distinct digits adding to 17 are 8 and 9 only. You have turned an awkward box into a unique pair without filling anything else.

Outies are often easier to see if you look at the border instead of the interior. Walk the edge of a box. Every time a dashed cage line crosses that edge, the cells on the far side are candidates for the outie set. If only one cell crosses, its value is the difference between the touching cage sums and 45. If two cells cross and they see each other, they are a combination. If they do not see each other, they can theoretically repeat, so you only know the sum, not the pair list. Check whether they share a row, column, or cage before you delete digits.

Two-cell innies and outies are the step that separates a medium puzzle from a hard one on this site. A single forced cell is a beginner 45. A forced pair, especially one that then points along a line, is the intermediate version. After you know the pair, treat it like any other unique cage: pencil both digits, then erase them from the houses that see both cells.

Bands are the same idea one size up. The three boxes across the top of the board sum to 135. Cages that leak into row 4 produce outies of that band. Hard puzzles like to leak two or three cells into the next band and leave you a sum such as 12 or 19. Split that sum with the combination table, then come back to the band with fewer candidates.

When you are stuck, do not scan for a clever digit. Scan the nine boxes for a border that is crossed once or twice. That tour takes less than a minute and it is the move most players skip.

Use this technique on a puzzle

Keep the combination table open while you read, and the rules if the cages themselves are still new.