How to Solve Sudoku: Rule of 45 (Killer)

Any row, column or box totals 45. Subtract the sums of the cages that fit inside it, and you know the sum of the cells left over.

Also known as innies and outies, in Killer Sudoku. On Puzzle Lounge it appears from Killer Hard up.

See it step by step

  1. Look at the centre box (1 to 9 add up to 45, so every row, column and box totals 45)
  2. 3 cages fit wholly inside (sums 15, 15 and 11)
  3. The cages total 15 + 15 + 11 = 41
  4. The one remaining cell is 45 − 41 = 4 (it is the cell in none of those cages)
  5. So this cell is 4 (5 and 8 go from row 6, column 4)

This is Killer Hard No.1, partly solved.

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How to find it

  1. Pick a row, column or box.
  2. Add up the sums of the cages that fit wholly inside it.
  3. Subtract that from 45: what is left is the sum of the cells outside those cages. It is easiest to find where only 1 or 2 cells are left.

Things to watch

  • Do not add a cage that is only half inside.
  • If 2 or more cells are left, think about the combinations for their sum.
Read the full explanation

Add 1 to 9 once each and you get 45. So every row, column and box totals 45. Subtract the sums of the cages that fit wholly inside it from 45, and you know the sum of the cells left over.

Suppose cages with sums 10, 14 and 17 fit wholly inside a box. Together they make 41.

The box totals 45, so the cells outside those cages add up to 45 − 41 = 4. If only one cell is left, it must be 4.

Conversely, when a cage sticks out of a box, subtract 45 from the cage's sum and you get the sum of the cells sticking out (outies). 2 rows or columns taken together make 90.

The cages that fit wholly inside the centre box total 15 + 15 + 11 = 41. The centre box totals 45, so the cell left, row 6, column 4, is 45 − 41 = 4.

Other techniques

Hidden SingleNaked SinglePointingClaimingHidden PairHidden TripleCage Combinations (Killer)Naked PairNaked TripleX-WingXY-WingSwordfishSkyscraper2-String KiteXYZ-WingW-WingJellyfish

For the basics and how to use notes, see how to solve sudoku, with tips. If you get stuck, the game's hints guide you step by step, starting with where to look.

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