Any tips/suggestions for this one?

*** 5** *18

8*4 *21 653

51* *83 *9*

*2* 81* *69

6*7 *52 381

18* **6 *4*

*6* 1*8 975

*58 2** 13*

7*1 **5 82*

Taken from Sudoku programme - very hard.

14 posts
• Page **1** of **1**

Any tips/suggestions for this one?

*** 5** *18

8*4 *21 653

51* *83 *9*

*2* 81* *69

6*7 *52 381

18* **6 *4*

*6* 1*8 975

*58 2** 13*

7*1 **5 82*

Taken from Sudoku programme - very hard.

*** 5** *18

8*4 *21 653

51* *83 *9*

*2* 81* *69

6*7 *52 381

18* **6 *4*

*6* 1*8 975

*58 2** 13*

7*1 **5 82*

Taken from Sudoku programme - very hard.

- Arnie
**Posts:**49**Joined:**19 May 2005

Ok, here is your current grid, with the candidates for the number 9 marked.

Now there are two X-wings, I'll the one which doesn't help you much, but it might learn you the technique which you can use to find the second one. (number 9 aswell)

To be able to speak of an X-Wing you first need to have only two cells for a certain number in a column).

If you find one such column then you haven't enough yet, you need to find another column which follows the same rule.

This does not nessesarily mean an X-wing though, there is an extra rule: the candidate-cells of the first column has to be on the same row as the candidate-cells of the second column.

To show you the example:

column 1: 9 is possible in r1c1 and r1c6.

column 6: 9 is possible in r8c1 and r8c6

As you can see the rows match so we have an X-wing.

This allows you to remove the 9 as a candiate from all other cells on row 1 and row 6.

Why? :

* Assume r1c1 is not 9, then r8c6 has to be 9, else it is impossible for column 6 to have a 9.

* Assume r1c6 is not 9, then r8c1 has to be 9, else it is impossible for column 1 to have a 9.

You see the pattern?

(Note: the same goes for rows too, just replace all instances of column with row, and all instances of row with column)

9? 9? 9? | 5 9? 9? | * 1 8

8 9? 4 | 9? 2 1 | 6 5 3

5 1 * | * 8 3 | * 9 *

-----------------------

* 2 * | 8 1 * | * 6 9

6 9? 7 | 9? 5 2 | 3 8 1

1 8 9? | 9? 9? 6 | * 4 *

-----------------------

* 6 * | 1 * 8 | 9 7 5

9? 5 8 | 2 9? 9? | 1 3 *

7 9? 1 | 9? 9? 5 | 8 2 *

Now there are two X-wings, I'll the one which doesn't help you much, but it might learn you the technique which you can use to find the second one. (number 9 aswell)

To be able to speak of an X-Wing you first need to have only two cells for a certain number in a column).

If you find one such column then you haven't enough yet, you need to find another column which follows the same rule.

This does not nessesarily mean an X-wing though, there is an extra rule: the candidate-cells of the first column has to be on the same row as the candidate-cells of the second column.

To show you the example:

column 1: 9 is possible in r1c1 and r1c6.

column 6: 9 is possible in r8c1 and r8c6

As you can see the rows match so we have an X-wing.

This allows you to remove the 9 as a candiate from all other cells on row 1 and row 6.

Why? :

* Assume r1c1 is not 9, then r8c6 has to be 9, else it is impossible for column 6 to have a 9.

* Assume r1c6 is not 9, then r8c1 has to be 9, else it is impossible for column 1 to have a 9.

You see the pattern?

(Note: the same goes for rows too, just replace all instances of column with row, and all instances of row with column)

- Animator
**Posts:**469**Joined:**08 April 2005

No...

Also, r1c2 cannot be 9... you can remove 9 as a candidate because of the previous X-Wing.

As in, what happens when r1c2 is 9? then r1c1 can't be 9, r1c6 can't be 9 either, and then r8c1 and r8c6 has to be 9... (else column 1 or column 6 does not have the number 9) which is impossible... the same number twice on one row?

The other X-Wing is in the rows... so start looking for rows with only two candidate-cells :)

Also, r1c2 cannot be 9... you can remove 9 as a candidate because of the previous X-Wing.

As in, what happens when r1c2 is 9? then r1c1 can't be 9, r1c6 can't be 9 either, and then r8c1 and r8c6 has to be 9... (else column 1 or column 6 does not have the number 9) which is impossible... the same number twice on one row?

The other X-Wing is in the rows... so start looking for rows with only two candidate-cells :)

- Animator
**Posts:**469**Joined:**08 April 2005

r2c2 r2c4, r9c2 r9c4 is correct :)

No, column 5 has four cells where the number 9 can go... an X-wing only works if there are exactly 2 cells.

Another column that has only two cells is column 3, but you will not find a matching column... If you would use column 3 then you need to find a column that fits the following constraint:

a) 9 is a possibility on row 1 (since r1c3 has the number 9 as a candidate)

b) 9 should be possible on row 6

c) there are only two cells in that column that can have the number 9

There is no column for which a, b and c is true...

could you not equally have chosen r1c5 and r8c5?? Is my xwing right?

No, column 5 has four cells where the number 9 can go... an X-wing only works if there are exactly 2 cells.

Another column that has only two cells is column 3, but you will not find a matching column... If you would use column 3 then you need to find a column that fits the following constraint:

a) 9 is a possibility on row 1 (since r1c3 has the number 9 as a candidate)

b) 9 should be possible on row 6

c) there are only two cells in that column that can have the number 9

There is no column for which a, b and c is true...

- Animator
**Posts:**469**Joined:**08 April 2005

Yes that's the one.

And it certainly has a usage:

Now you know that either r2c2 and r5c4 has the number 9, or r2c4 and r5c2. No other cell in column 2 nor column 4 can have the number 9.

This allows you to remove 9 from the list of candidates from: r1c2, r6c4, r9c2 and r9c4. If you fill in the number 9 in one of those four cells then you are unable to solve the puzzle (feel free to try!).

Now there is only one place left where the number 9 can go on row 9.

(You could do the same for the first X-Wing and then you will find that there is only one place for the number 9 in column 3)

And it certainly has a usage:

Now you know that either r2c2 and r5c4 has the number 9, or r2c4 and r5c2. No other cell in column 2 nor column 4 can have the number 9.

This allows you to remove 9 from the list of candidates from: r1c2, r6c4, r9c2 and r9c4. If you fill in the number 9 in one of those four cells then you are unable to solve the puzzle (feel free to try!).

Now there is only one place left where the number 9 can go on row 9.

(You could do the same for the first X-Wing and then you will find that there is only one place for the number 9 in column 3)

- Animator
**Posts:**469**Joined:**08 April 2005

14 posts
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