Example of a '1 In and 1 Out'

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This is a version 14.0 screenshot

1 In and 1 Out:

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 has one missing Square and one extra Square. The difference in values of these two Square can then be determined, causing some of the possibles in the two Squares to be impossible solutions.

In this example, the Killer Groups outlined in red form a set consisting of the top-right Box plus D7 and missing B7. The set of Killer Groups sums to 47. Since the top-right Box must sum to 45 (the 45 rule), then D7 must be 2 greater than B7, causing a number of impossible solutions (outlined in orange) which can be removed.




Second Example of a '1 In and 1 Out'

Screenshot
This is a version 14.0 screenshot

1 In and 1 Out:

In this second example, the Killer Groups outlined in red form a set consisting of the top two Rows plus C5 minus B8. The set of Killer Groups sums to 97. Since the top two Rows must sum to 90 (2 X the 45 rule), C5 must be 7 greater than B8, causing a number of impossible solutions (outlined in orange) which can be removed.




Third Example of a '1 In and 1 Out'

Screenshot
This is a version 14.0 screenshot

1 In and 1 Out:

In this third example, the Killer Groups outlined in red form a set consisting of the top-left and middle-left Boxes plus A4 minus B3. The set of Killer Groups sums to 97. Since the two Boxes must sum to 90 (2 X the 45 rule), A4 must be 7 greater than B3, causing a number of impossible solutions (outlined in orange) which can be removed.