Step 17 · Master
What is Innie-Outie Difference? How to Solve Killer Sudoku
A step beyond the Rule of 45: it finds the difference between a cell missing inside a row, column, or box and a cell sticking out, which narrows down both numbers.
What it is
A step beyond the Rule of 45. From the total of a row, column, or box, take away the cages inside it and the cages that stick out, counted in full.
What's left is the difference between the cells missing inside and the cells sticking out. If that's one cell each, you know how much bigger one is than the other.
Example: if the difference is 2, the inside cell is 2 more than the outside cell. If the outside cell is 1–3, the inside cell must be 3–5.
How to spot it
Use it when the Rule of 45 leaves one innie and one outie whose totals you can't work out separately. Add the sticking-out cages in full and count which cells are missing and which are extra.
Example
Dotted outlines are cages, with their total in the top-left corner. Yellow cells are where to look, orange cells are the reason, red digits are candidates you can remove, and the green digit is the answer.
The numbers in box 5 add up to 45. Take the cages completely inside (total 17) and add the cages that stick out (the 17-cage at R3C5, total 17) in full: that misses R5C4, R5C6, and R6C6 inside the area and includes R3C5 outside it. So (R5C4, R5C6, and R6C6) − (R3C5) = 45 − 17 − 17 = 11. Leaving out the numbers already placed, R5C4 − R3C5 = 7. So R5C4 is 7 more than R3C5. Numbers with no partner in the other cell (2, 3, 4, 5, 6, 7, 8, and 9) can't go in R5C4 and R3C5.