Step 4 · Easy
What is Rule of 45 (Innies & Outies)? How to Solve Killer Sudoku
Uses the fact that every row, column, and box adds up to 45: subtract the cages that fit inside to find the total of the cells that stick in or out.
What it is
Every row, column, and box holds 1–9 once each, so its numbers always add up to 45.
Subtract the totals of the cages that fit completely inside a box from 45, and you get the total of the remaining cells (the parts of cages that stick in from outside). If only one cell remains, its number is decided.
In the same way, you can work out the total of the cells that stick out of the box from the cages that cross its edge.
How to spot it
Look for a row, column, or box where the cages almost fit, with only one or two cells poking in or out. Add up the cages inside and compare with 45.
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.
Each row, column, and box holds 1–9 once, so the numbers in box 2 add up to 45, and the cages completely inside total 19. So the inside parts of the cages that stick out (the 16-cage at R1C3 and the 18-cage at R3C4) add up to 45 − 19 = 26. Those cages total 34, so the cells sticking out (R1C3 and R4C4) add up to 34 − 26 = 8. The ways to make 8 with these 2 cells (R1C3 and R4C4) that fit the candidates are 1+7, 2+6, and 3+5. Numbers in none of them (4, 8, and 9) can't go in R1C3 and R4C4.