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# Solving Techniques 15 Unique Rectangles

The cells that that contain [12] in the diagram below would work as both:
1 2
2 1
or
2 1
1 2
It can be either solution.
We presume that a Sudoku problem can’t have two solutions.

[34], on the other hand, can’t be switched around. They wouldn’t be switched within the same box, so the numbers can’t be switched.

## Unique Rectangles 1

Like the diagram, this is a pattern where the [12] can be switched around. If it can be switched, it wouldn’t work as a Sudoku problem, so in the cells indicated in red, either a [3] or [4] is entered.

## Unique Rectangles 2

In this pattern, one of the upper two cells with [123], will definitely be a [3]. Hence, [3] won’t go in the cell marked red and it will be a [4].

## Unique Rectangles 3

In this pattern, one of the lower two cells with [123], will definitely be a [3]. That means, [3] can’t be in the other cells in the box. Also, a [3] can’t be entered in line H of the boxes to the left and right.

## Unique Rectangles 4

An [8] or [9] will definitely be entered in either the [129] cell or [1289] cell. There is a cell at the very bottom with [89] as candidates. If an [8] is entered in the blue cell above, then the pink cell will be a [9]. If the blue cell is a [9], then the pink cell will be an [8], so [8] or [9] can’t be entered in the cells marked with X’s.

## Unique Rectangles 5

An [8] or [9] will definitely be entered in the [128] cell or [129] cell. The pink cell only has [89] as candidates. This means if an [8] or [9] is entered into either one of the blue cells, the pink cells will become [8] or [9], so [8][9] can’t be entered into the cells marked with X’s.

## Unique Rectangles 6

An [8] or [9] will go into either one of the [128][129] cells below. However, there are no open cells in this line where a [1] can be entered. Therefore, a [1] will have to go in one of the blue cells below, so a [2] can’t be entered into one of the blue cells at the bottom.

## Unique Rectangles 7

Lets examine the [128][129] cells. In this line, a [1] can’t be entered into any of the empty cells. This means, in either one of the [128][129] cells a [1] has to be entered, and [2] can be eliminated as a candidate.

## 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