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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)

## 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

 A1 A2 A3 A4 A5 A6 A7 A8 A9 B1 B2 B3 B4 B5 B6 B7 B8 B9 C1 C2 C3 C4 C5 C6 C7 C8 C9 D1 D2 D3 D4 D5 D6 D7 D8 D9 E1 E2 E3 E4 E5 E6 E7 E8 E9 F1 F2 F3 F4 F5 F6 F7 F8 F9 G1 G2 G3 G4 G5 G6 G7 G8 G9 H1 H2 H3 H4 H5 H6 H7 H8 H9 I1 I2 I3 I4 I5 I6 I7 I8 I9