Rooted: Created page with "This is a medium-level solving technique specific to Killer Sudoku. It usually only comes into play with more difficult puzzles. When a set of cages lies nearly &..."

2020-06-04T02:37:02Z

Created page with "This is a medium-level solving technique specific to Killer Sudoku. It usually only comes into play with more difficult puzzles. When a set of cages lies nearly &..."

New page

This is a medium-level [[solving technique]] specific to [[Killer]] [[Sudoku]]. It usually only comes into play with more difficult puzzles.

When a set of cages lies nearly – but not exactly – within one or more [[house]]s, sometimes there is a mix of cells that hang outside the house(s) ([[outie]]s) and cells that are within the house(s) but outside of the cages ([[innie]]s). By calculating the '''innie-outie difference''' (the difference between the sum of the innies and the sum of the outies), we may [[eliminate]] [[candidate]]s from the innie and outie cells.

This technique is usually only useful when few cells are involved, or when the difference between the innies and outies is very large. Typically, in a given puzzle, there are many possible innie-outie differences, most of which yield no useful information; but the patient solver may stumble upon one that helps crack the puzzle.

== Example ==
This is the starting position of [http://sudocue.net/weeklykiller.php?id=7 Assassin 7] by [[User:Ruud|Ruud]]'s ''Weekly Assassin Killer Sudoku''.

[[Image:InnieOutieDifference.png]]

Consider [[column]] 9, the innie marked yellow and the outie marked green. Let ''S'' be the sum of the [[cell]]s in column 9 sans the innie (i.e. R23456789C9), ''I'' be the value of the innie, and ''O'' be the value of the outie. By the [[45 rule]] on the entire column, we have
''S'' + ''I'' = 45

On the other hand, the selected cages give
''S'' + ''O'' = 16 + 14 + 9 = 39

Subtracting one equation from the other, we get the innie-outie difference
''I'' - ''O'' = 6

As the innie ''I'' can only be 8 or 9, we find that the outie ''O'' can only be 2 or 3. Thus all other candidates (1, 4, 5, 6, 7, 8, 9) can be eliminated from the outie.

[[Category:Killer Sudoku]]
[[Category:Solving Techniques]]

Innie-outie difference - Revision history

Rooted: Created page with "This is a medium-level solving technique specific to Killer Sudoku. It usually only comes into play with more difficult puzzles. When a set of cages lies nearly &..."