Example of a Three Squares

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This is a version 14.0 screenshot

Three 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 three squares (or has three extra squares). The total of these three squares can then be determined, causing some of the possibles in the three squares to be impossible solutions.

In this example, the Killer Groups outlined in red form a set consisting of the upper-left Box plus the three squares A4, B4 and C4. The set of Killer Groups sums to 67. Since the upper-left Box must sum to 45 (the 45 rule), the three squares must sum to 22, causing a number of impossible solutions (outlined in orange) which can be removed.




Second Example of a Three Squares

Screenshot
This is a version 14.0 screenshot

Three Squares:

In this second example, the Killer Groups outlined in red form a set consisting of Columns 1-3 plus the three squares A4, C4 and D4. The set of Killer Groups sums to 142. Since Columns 1-3 sum to 135 (3 X the 45 rule), the three squares must sum to 7, causing a number of impossible solutions (outlined in orange) which can be removed.




Third Example of a Three Squares

Screenshot
This is a version 14.0 screenshot

Three Squares:

In this third example, the Killer Groups outlined in red form a set consisting of the top-right and the middle-right Boxes, minus the three squares A7, B7 and F7. The set of Killer Groups sums to 73. Since the two Boxes sum to 90 (2 X the 45 rule), the three squares must sum to 17, causing a number of impossible solutions (outlined in orange) which can be removed.