Innies and Outies — Killer Sudoku Technique
When cages straddle the edges of a row, column, or box, the boundary cells inside (innies) and outside (outies) the unit carry known partial sums.
Killer Sudoku sudoku technique
What it is
An INNIE is a cell INSIDE a row, column, or box that belongs to a cage extending OUTSIDE the unit. An OUTIE is the mirror: a cell OUTSIDE the unit belonging to a cage that REACHES INTO it. When a unit has cages of both kinds, the 45 rule lets you isolate the sum of just the innies or just the outies. For a unit U with N cells, let S_in = sum of cages fully inside U and S_cross = sum of cages crossing U's boundary. The innies sum to (45 − S_in) − (cells of crossing cages outside U). Rearranging gives the outies sum directly. A SINGLE innie or outie locks one digit; a MULTI-cell innie/outie tightens candidates and often combines with the combinations cheat sheet to eliminate digits.
When to use it
After the 45 rule has placed the easy cells, look for rows, columns, or boxes with exactly one or two innies/outies. Single innies/outies place a digit immediately; double innies/outies typically eliminate 4–6 candidates.
Worked example
Box 1 contains three fully-inside cages summing to 30 (say 12 + 9 + 9) and a 12-cage covering R3C3 (inside box 1) and R4C3 (outside box 1, in box 4). The single innie is R3C3 and the single outie is R4C3. By the 45 rule: R3C3 + (30) + (12 − R4C3) cells inside box 1 = 45. Since R4C3 + R3C3 = 12 (the cage), R3C3 = 45 − 30 − (12 − R3C3) does not simplify directly — but combined with R3C3 ≤ 9 and R4C3 ≤ 9, the constraint pins R3C3 to {3, 4, ..., 9}, dropping 1 and 2 from its candidates.
Try it
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