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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

R1C1R1C2R1C3R1C4R1C5R1C6R1C7R1C8R1C9
R2C1R2C2R2C3R2C4R2C5R2C6R2C7R2C8R2C9
R3C1R3C2R3C3R3C4R3C5R3C6R3C7R3C8R3C9
R4C1R4C2R4C3R4C4R4C5R4C6R4C7R4C8R4C9
R5C1R5C2R5C3R5C4R5C5R5C6R5C7R5C8R5C9
R6C1R6C2R6C3R6C4R6C5R6C6R6C7R6C8R6C9
R7C1R7C2R7C3R7C4R7C5R7C6R7C7R7C8R7C9
R8C1R8C2R8C3R8C4R8C5R8C6R8C7R8C8R8C9
R9C1R9C2R9C3R9C4R9C5R9C6R9C7R9C8R9C9

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