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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.

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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

A1A2A3A4A5A6A7A8A9
B1B2B3B4B5B6B7B8B9
C1C2C3C4C5C6C7C8C9
D1D2D3D4D5D6D7D8D9
E1E2E3E4E5E6E7E8E9
F1F2F3F4F5F6F7F8F9
G1G2G3G4G5G6G7G8G9
H1H2H3H4H5H6H7H8H9
I1I2I3I4I5I6I7I8I9

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