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Solving Techniques 16
Extended Unique Rect.

This is a three-cell version of the Unique Rectangles.
In the diagram below, either [123][231][312] or [312][123][231] would work as solutions.
We presume that a Sudoku problem can’t have two solutions.

The diagram below examines how many combinations of [123] there are. There are 12 patterns that have multiple solutions.

Also, [123][123][23] or [12][123][123] or [123][12][23] are extended unique rectangles.
Further, [12][23][13] are also extended unique rectangles.

Extended Unique Rect. 1

In the diagram below, the yellow part becomes [8][9]. Otherwise, we have an extended unique rectangle, which has multiple solutions.

Lets examine below. If the solution only contained the red 8, the other cells will become the yellow candidates, creating an extended unique rectangles.

If, as below, only the red [9] was in the solution, then too, the other cells will become the yellow candidates, creating an extended unique rectangles. Therefore, [8][9] are both confirmed. (Otherwise, we are left with multiple solutions)

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Extended Unique Rect. 2

The pink [139] cell will be a [9].

Extended Unique Rect. 3

The pink [1289] cell will be [8] or [9].

Extended Unique Rect. 4

The pink [139] cell will be a [9].

Names of cells in Sudoku

A1A2A3A4A5A6A7A8A9
B1B2B3B4B5B6B7B8B9
C1C2C3C4C5C6C7C8C9
D1D2D3D4D5D6D7D8D9
E1E2E3E4E5E6E7E8E9
F1F2F3F4F5F6F7F8F9
G1G2G3G4G5G6G7G8G9
H1H2H3H4H5H6H7H8H9
I1I2I3I4I5I6I7I8I9

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