Solved Exercise on How To Solve Sudoku Puzzles: 9

1 6

3,4,

5,6 6,7

6,9

8,9

3,4

Cells (4,3), (5,1), (5,2) and (6,3) can take only one of the values '6', '7', '8', or '9' among themselves. So, we can eliminate these 4 values from the other Cells in the Left Center Major Square, applying the Hidden

Subsets Approach for How To Solve Sudoku Puzzles. So, the value '6' gets eliminated from the Cells (4,1) and (6,1). Now, we have:

Let's now look at the possible Cells for the value '6' in the Top Left and Mid Left Major Squares, as well as Columns 1 and 3. Let's color them all green, initially.

We see that, if Cell (1,3) takes value '6', then Cell (1,1), (3,1) , (4,3) and (6,3) can't be 6 which, means that C1 and Mid Left Major square can't

have a value '6' at all. So, Cell (1,3) can't have '6'. So, we can eliminate the value '6' from Cell (1,3)

We now have: If we see carefully, we notice that there are a series of 2-possible-value-

Cells and all of them are interconnected starting from Cell (1,3) in some way. Let's explore.

Let's see the Cells (1,3) ,(4,3) , (4,6) and (4,1) colored below:

Solved Exercise on How To Solve Sudoku Puzzles: 9

1 6

1 ..

7,8

3,6

6,3

6,9

Here, if Cell (1,3) takes the value '9', then Cell (4,3) takes the value '6', consequently Cell (4,6) takes the value '3' and Cell (4,1) should, therefore, take the value '5'.

We've added 'X' to the 3 Cells because we're not fixing the other value marked in red to these Cells yet.

What if Cell (1,3) takes the value '8'? Let's see a different set of 2- possible-value-Cells connected.

Consider the sequence of values in Cells as below:

(1,3) -> (1,6) -> (4,6) -> (4,3) -> (4,7) -> (9,7) -> (1,7) -> (3,9) -> (3,1) -

> (4,1)

If Cell (1,3) takes '8' then other Cells values are forced. Cell (1,6) takes

'3', Cell (4,6) takes '6' ,Cell (4,3) takes '9', Cell (4,7) takes '2', Cell (9,7)

takes '6', Cell (1,7) takes '9', Cell (3,9) takes '6', Cell (3,1) takes '3' and

Cell (4,1) takes value '5'.