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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
| 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 |
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