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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

R1C1R1C2R1C3R1C4R1C5R1C6R1C7R1C8R1C9
R2C1R2C2R2C3R2C4R2C5R2C6R2C7R2C8R2C9
R3C1R3C2R3C3R3C4R3C5R3C6R3C7R3C8R3C9
R4C1R4C2R4C3R4C4R4C5R4C6R4C7R4C8R4C9
R5C1R5C2R5C3R5C4R5C5R5C6R5C7R5C8R5C9
R6C1R6C2R6C3R6C4R6C5R6C6R6C7R6C8R6C9
R7C1R7C2R7C3R7C4R7C5R7C6R7C7R7C8R7C9
R8C1R8C2R8C3R8C4R8C5R8C6R8C7R8C8R8C9
R9C1R9C2R9C3R9C4R9C5R9C6R9C7R9C8R9C9

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