## Help sought please with very hard puzzle.

Advanced methods and approaches for solving Sudoku puzzles

### Help sought please with very hard puzzle.

I wonder whether anyone can help me with a small clue to take me forward with the Very Hard puzzle shown below? I try to complete one Very Hard puzzle each day and have completed three in a row (a big deal for me!) but the puzzle that I have posted has me baffled.

8** 634 *1*
**4 721 ***
*1* 589 ***

291 843 657
*58 2*6 *3*
6*3 9*5 82*

1** *58 *6*
*** *97 1**
*** 162 **5

Regards.

Zeb
zebedee

Posts: 26
Joined: 27 March 2005

First, look at where the candidates 5 and 9 can go in block 1. You should be able to make some eliminations in block 1 based on that information. Then you can look for an x-wing.
scrose

Posts: 322
Joined: 31 May 2005

Thanks scrose. I completely missed the 5/9 pairs!

I can't seem to see a viable X-wing. Can you narrow down the field for me please?

Regards.

Zeb
zebedee

Posts: 26
Joined: 27 March 2005

The x-wing is in the 9's.
scrose

Posts: 322
Joined: 31 May 2005

Thanks for replying scrose but I still can't see an X-wing in the 9s. Are there any other pointers you can add please?

Zeb
zebedee

Posts: 26
Joined: 27 March 2005

Sorry Zeb, I wasn't sure how specific you wanted the clue to be. Look at where the candidate 9's are in columns 1 and 8. This should let you eliminate some candidate 9's from rows 2 and 9.
scrose

Posts: 322
Joined: 31 May 2005

Are you saying scrose that the X-Wing comprises c1/r2, c8/r2, c1/r9 and c8/r9? If so, I don't see how this can be an X-wing since, according to my pencil marks, 9s can still go in c7/r2 and c7/r9. It would also seem that a 9 can go in c3/r9 as well.

Confusion reigns - at least in my mind.

Zeb

zebedee

Posts: 26
Joined: 27 March 2005

zebedee wrote:Confusion reigns - at least in my mind.

X-wings tend to unfortunately have that effect. I was tearing my hair out over the first puzzle I encountered with an x-wing.

zebedee wrote:Are you saying scrose that the X-Wing comprises c1/r2, c8/r2, c1/r9 and c8/r9?

Yes, that's correct.

zebedee wrote:If so, I don't see how this can be an X-wing since, according to my pencil marks, 9s can still go in c7/r2 and c7/r9. It would also seem that a 9 can go in c3/r9 as well.

Those candidate 9's in r2c7 and r9c7 are the ones that you can eliminate due to the candidate 9's in r2c1, r2c8, r9c1, and r9c8.

For a moment, focus only on the candidate 9's in rows 2 and 9.

Code: Select all
` . . . | . . . | . . . 9 . . | . . . | 9 9 9 . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . 9 . 9 | . . . | 9 9 .`

Suppose we place a 9 at r2c1. That would eliminate the remaining candidate 9's in row 2 in block 3, and the candidate 9 at r9c1.

Code: Select all
` . . . | . . . | . . . 9 . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . 9 | . . . | 9 9 .`

Note this would leave the candidate 9 at r9c8 as the only candidate 9 in column 8. Thus the other candidate 9's in row 9 can be eliminated.

Code: Select all
` . . . | . . . | . . . 9 . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . 9 .`

So, that is one diagonal wing of the x-wing. Let's look at the other possibility.

Code: Select all
` . . . | . . . | . . . 9 . . | . . . | 9 9 9 . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . 9 . 9 | . . . | 9 9 .`

Suppose we place a 9 at r2c8. That would eliminate the remaining candidate 9's in row 2, and the candidate 9 at r9c8.

Code: Select all
` . . . | . . . | . . . . . . | . . . | . 9 . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . 9 . 9 | . . . | 9 . .`

Note this would leave the candidate 9 at r9c1 as the only candidate 9 in column 1. Thus the other candidate 9's in row 9 can be eliminated.

Code: Select all
` . . . | . . . | . . . . . . | . . . | . 9 . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .-------+-------+------- . . . | . . . | . . . . . . | . . . | . . . 9 . . | . . . | . . .`

This is the other diagonal wing of the x-wing.

That means the only place 9 can be in row 2 is either in column 1 or 9 and the only place 9 can be in row 9 is either in column 1 or 9.

I hope this helped!
scrose

Posts: 322
Joined: 31 May 2005

Many thanks for taking the trouble to write at such length scrose. It was very helpful and much appreciated.

I eventually solved the puzzle.

Zeb

zebedee

Posts: 26
Joined: 27 March 2005