Let's learn this thru an Example on How To Solve Sudoku Puzzles:

Approach for How To Solve Sudoku Puzzles 3

2 4

5 3

? ? ? ? ?

Cells (3,4), (3,5), (3,6), (3,7), (3,8) and (3,9), marked '?' in red, can't take the value '6'.

Why? Because, the Top Major Square still needs a '6'; and leaving out the already occupied Cells and the Cells in column 3 (because Column

3 already has a '6') in the Top Major Square, the only 2 possible positions for the value '6' are Cells (3, 1) and (3, 2). In either case, no

other Cell in Row 3 can take the value '6'. Interchanging (and slightly modifying) Rows & Columns, you may have the pattern as below:

Approach for How To Solve Sudoku Puzzles 3

2 4

3 5

This is called 'Direct Interaction' or 'Row/Column-Major Square Interaction' or 'Row/Column-Block Interaction' Approach for How To Solve Sudoku Puzzles.

Approach for How To Solve Sudoku Puzzles 3

Pattern to look for: A Rectangular pattern of Cells filled up in a Major Square; a particular value not yet filled up in the above Major Square being found on one side of it horizontally or vertically, in the Row/ Column that has Cells to be filled in.et's see a situation that's similar to the above, but this time, it is across 2 Major Squares instead of Row/Column-Major Square.

Here, though a certain value is not yet there in a Major Square, L you can still eliminate that value from a set of Cells in the adjoining

Major Squares (i.e., in the same Rows/ Columns). This is because we may not yet have reached the stage where we can fix that value to any specific Cell in that Major Square, but yet, from the interactions with the other Major Squares, and from the occupied values in the Major Square, it is clear that soon a Cell in that Major Square would definitely take the value. So, you can rule out the chances of other Cells in that

Row (or Column) taking the same value.

Approach for How To Solve Sudoku Puzzles 4

Let's see this thru an Example on How To Solve Sudoku Puzzles:

2 9 8

Here, both the Top Right and Bottom Right Major Squares still need a '5'. Given the puzzle above, the only candidate Cells for '5' in the Top

Right Major Square are Cells (3, 8) and (3, 9). And the only candidate

Cells for '5' in the Bottom Right Major Square are Cells (7, 9) and (8,

8). Whichever of these Cells takes the value '5' in these 2 Major Squares, it is clear that there's no place for another '5' in these 2 Columns in the Mid Right Major Square. So, we can eliminate the possibility of value '5' from being allotted to Cells (4, 8), (4, 9), (5, 8), (5, 9), (6, 8), and (6, 9), And '5' in this Major Square can only appear in one of the 3 Cells (4,7), (5,7) and (6,7), marked '?' in black.

This is called or Approach for How To Solve Sudoku Puzzles. all marked '?' in red.

'Indirect Interaction' 'Major Square-Major Square Interaction' 'Block-Block Interaction'

Approach for How To Solve Sudoku Puzzles 4

Pattern to look for: There are 3 Major Squares, all at the Top/ Middle/ Bottom/ Left/ Centre/ Right. All these 3 Major Squares still need a certain value, which is actually present in a Major Square

perpendicular to (i.e., by the side of) two of them.

If, among the possible set of values that a Cell can take, one or more values have been taken by one or more Cells in its Row/ Column/Major Square, then you can rule out these values for the Cell. This is just the same as the Reduction Approach for How To Solve Sudoku Puzzles that we've seen in the

Possibility Matrix Method.

Though we've learnt this in the Possibility Matrix Method, for the sake of completeness, let's see this thru an Example on How To Solve Sudoku Puzzles:

Let's say that through other inferences, we know that Cell (5,5) can only take the values {4,5,6,7}, and the values '4, '5', '6' were obtained successfully only in the last step.

Now, Cell (5,5) can take only the value '7', as below.

Approach for How To Solve Sudoku Puzzles 5

4,5,6,7

This is called the 'Reduction' Approach for How To Solve Sudoku Puzzles.

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