Example of a Four Squares

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This is a version 14.0 screenshot

Four Squares:

Taking advantage of 'The 45 Rule' (every Row, Column and Box consists of the numbers 1 to 9 and so must sum to 45), this analysis looks for a set of Rows, Columns or Boxes that is missing four squares (or has four extra squares). The total of these four squares can then be determined, causing some of the possibles in the four squares to be impossible solutions.

In this example, the Killer Groups outlined in red form a set consisting of the lower left Box plus the four squares F4, G4, H4 and H5. The set of Killer Groups sums to 67. Since the lower left Box must sum to 45 (the 45 rule), the four squares must sum to 22, causing a number of impossible solutions (outlined in orange) which can be removed.




Second Example of a Four Squares

Screenshot
This is a version 14.0 screenshot

Four Squares:

In this second example, the Killer Groups outlined in red form a set consisting of Columns 1-4 plus the four squares A5, A6, A7 and H5. The set of Killer Groups sums to 200. Since Columns 1-4 sum to 180 (4 X the 45 rule), the four squares must sum to 20, causing a number of impossible solutions (outlined in orange) which can be removed.




Third Example of a Four Squares

Screenshot
This is a version 14.0 screenshot

Four Squares:

In this third example, the Killer Groups outlined in red form a set consisting of Columns 6-9 minus the four squares A6, A7, J6 and J7. The set of Killer Groups sums to 157. Since Columns 6-9 sum to 180 (4 X the 45 rule), the four squares must sum to 23, causing a number of impossible solutions (outlined in orange) which can be removed.