Pattern to look for: A certain value that can be taken by only one of 2 Cells in certain Row, and the same value can be taken by only one of 2 Cells in the same Columns in another Row. That is, four Cells falling in 2 identical Rows and Columns share a prospective value. (This is also true of Four Cells falling in 2 identical Rows and Major Squares, OR, in 2 identical Columns and Major Squares).his is similar to the previous Approach for How To Solve Sudoku Puzzles, but in 3 Rows (or Columns). Here, there are 2 candidates for a value in each Row (or Column). And these candidates fall in the same set T of 3 Columns (or Rows). Then, you can rule out this value from the other Cells in their Columns (or Rows).

We'll see this thru an Example on How To Solve Sudoku Puzzles.

Where 'x', 'y', 'z', 'p” 'q', and 'r' are any values (and 'A', 'B', 'M', 'N', and 'L') are any set of values, and '4' is not a possible value in any other

Cell in these Rows (3, 4 and 9), you can eliminate the value '4' from the possible set of values ({A,4}, {B,4}, {M,4}, {N,4}, and{L,4}) in all other cells in these Columns.

Approach for How To Solve Sudoku Puzzles 9

A, 4

M,4

y, 4

N, 4

q, 4

x, 4

L, 4

z, 4

B, 4

p, 4

r, 4

Let's see what the given situation means. This means that either Cell (3,2) or Cell (3,3) must be a '4'; and, either Cell (4,3) or Cell (4,9) must be a '4'; and, either Cell (9,2) or Cell (9,9) must be a '4'.

However, if Cell (3,2) is a '4', Cell (3,3) can't be a '4' and Cell (9,2) can't be a '4' either. The only Cell in R9 that can be a '4' is (Cell (9,9); so,

Cell (4,9) can't be a '4'. Since R4 still needs a '4', Cell (4,3) must be a '4'.

Alternatively, if Cell (3,3) is a '4', Cell (4,3) can't be a '4', and Cell (3,2)

can't be a '4' either; Since R4 needs a '4', Cell (4,9) must be a '4', which means Cell (9,9) can't be a '4'. Since R9 needs a '4', Cell (9,2) must be a '4'.

Let's now see what this boils down to Column-wise: Either Cell (3,2) is a '4' or Cell (9,2); and, either Cell (3,3) is a '4' or Cell (4,3); and, either Cell (3,9) is a '4' or Cell (9,9).

That is, one of the Cells in each of these Columns is a '4'. So, no other Cell in these Columns can be a '4'.

So, ({A,4}, {B,4}, {M,4}, {N,4}, and{L,4}) reduce to ({A}, {B}, {M}, {N}, and{L}).

Approach for How To Solve Sudoku Puzzles 9

This is called . You can have the Rows and Columns interchanged here, and this Approach for How To Solve Sudoku Puzzles is still applicable.

'Sword-Fish' Approach for How To Solve Sudoku Puzzles

Approach for How To Solve Sudoku Puzzles 9

Pattern to look for: Six Cells falling in 3 identical Rows and Columns share a prospective value.

This is also somewhat similar to the previous ones in the sense that it helps eliminate certain possibilities based on 'not so apparent' logic.

The logic here is that, if you have a row-column, (or) row-major square (or) column-major square intersection where 4 (or more) cells have a xy, x-z, y-z formation, you can rule the possibility of 'z' in the fourth  Cell. Here, x, y and z represent a specific value between '1' and '9'.

Cell (2, 3) can be only 'x' or 'y'. Let's say it is 'x'. Then, Cell (2, 8) has to be 'z'. Then, Cell (7, 8) can't be 'Z'.

On the other hand, let's say Cell (2, 3) is 'y'. Then, Cell (7,3) has to be 'z', and so, Cell (7, 8) can't be 'Z'.

So, in any case, Cell (7, 8) can't be 'z', whenever we have a formation like this. So, we can see that we can eliminate 'z' from Cell (7, 8), as

Approach for How To Solve Sudoku Puzzles 10

p,z

x,y x,z

y,z

below:

Example on How To Solve Sudoku Puzzles:

Approach for How To Solve Sudoku Puzzles 10

5, 7

1, 4 4, 5

1, 5

p

x,y x,z

y,z

Reduces to This is called . We have seen only the case of rowcolumn interaction. The same obviously holds true for row-major square interaction and column-major square interaction. ''XY-Wing' Approach for How To Solve Sudoku Puzzles

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