The New Sudoku Players' Forum

[Guest]

I'll like to ask Duncan as to his thinking behind the placement of a 4 in (6,7) and a 2 in (9,5)?

I've been on this, starting from scratch, for about an hour and I cannot see how he reached his conclusions.

I see from your latter posts you got the 4 worked out.

I'd have to start the thing again to tell you how I got the 2 in 9,5 but then I run the risk of having to kill myself. Did you get it yet?

Duncan

Only just got up,work and sleep since my last message.
Duncan I see how you got the 2 in (9,5) although I put in the 3 (8,4) first.
No need of termination.

Jonas and Su-doku, what you are doing is trial and error, this is not necessary. 3 cannot go in (8,6), look to the 5 and 7's in column 6.
Once you've sorted out where the 3 goes in row 8, look to what can go in (5,7).

I finally cracked it last night, 1.30am.
Made a silly mistake after putting in the 3 in row 9, left a pencilmark un-erased and hit a brick wall, but once I spotted my mistake downhill all the way.

[Guest]

Still not awake

In the last message I meant put the 3 in ROW 8 not row 9

[Duncan]

Only just got up,work and sleep since my last message.
Duncan I see how you got the 2 in (9,5) although I put in the 3 (8,4) first.
No need of termination.

Jonas and Su-doku, what you are doing is trial and error, this is not necessary. 3 cannot go in (8,6), look to the 5 and 7's in column 6.
Once you've sorted out where the 3 goes in row 8, look to what can go in (5,7).

I finally cracked it last night, 1.30am.
Made a silly mistake after putting in the 3 in row 9, left a pencilmark un-erased and hit a brick wall, but once I spotted my mistake downhill all the way.

Are we all agreed then, that this VHard was a pain in the a***?

Duncan

[paulf2127]

Ok, I have reached the following, both via my own sweat and a hint about the subset in column 6 from the forum;

x 2 7 | 8 x x | x 5 x
x 8 3 | x 5 x | 7 9 1
5 x x | 7 x x | x 2 x
=============
x x 8 | x x x | 5 x 6
x 1 x | x 4 x | x 8 x
7 x 5 | x 8 x | 4 x x
=============
x 5 x | x x 9 | x x x
8 6 9 | 3 1 x | 2 4 x
x 7 x | x 2 8 | x 6 x

Now what?

[Animator]

I suggest re-reading the thread...

since that is the exact same grid that was original posted... (or atleast one of the two, the first one where just the clues).

[paulf2127]

I have done animator. I see you think the solution is a mix between an xwing, column 6 and column 9.


I have r5c6 [5,7], r5c9 [279]

I have r8c6 [5,7], r8c9 [5,7]

Am I missing something obvious I can eliminate from these four cells? Or am I just dim. I tell you what, after playing with these very hards and searching for the sometimes single clue that you need to move forward - the finedish ones are not much of a challenge lately!

[paulf2127]

I've seen it. I am dim. Solved.

[ExpertNovice]

Here is where I'm at the moment.

*27|8**|*5*
*83|*5*|791
5**|7**|*2*
**8|***|5*6
*1*|*4*|*8*
7*5|*8*|4**
*5*|**9|***
869|*1*|24*
*7*|**8|*6*

I've managed to solve the placement of 4 in (6,7) by using a x-wing of 7's in cells (5,6)(5,9)(8,6)(8,9) this eliminates the 7 in (7,9) leaving the possibles in column 9 of: 3,4 in (1,9), 3,4,8 in (3,9) and 3,8 in (7,9) you can now eliminate the 4 in (6,9) leaving (6,7) the only position for a 4.

This is a very old thread but I hope someone can help me understand one issue. I don't understand how cells (5,6)(5,9)(8,6)(8,9) make an x-wing of 7's.

My notes indicate these cells still have the possibilities of
(2357) (2379)
( 357) (357)

If my notes are correct then those cells could be filled with 2, 9, 3, & 5, respectively (without looking at the effects of other cells).

Question 1: Why is it an x-wing of 7's?
Question 2: Is it also an x-wing of 3's?


PS. Sudoku was just "discovered" on Friday so obviously I have a lot of learning. I do understand x-wings but only on the most simple of levels and hope that this seemingly difficult version of an x-wing will help me understand them better.

Thanks.

[rubylips]

My notes indicate these cells still have the possibilities of
(2357) (2379)
( 357) (357)

That's right. The candidate grid is as follows:

Code: Select all

  1|4|6|9      2      7 |          8    3|6|9  1|3|4|6 |    3|6      5      3|4
      4|6      8      3 |        2|6        5    2|4|6 |      7      9        1
        5    4|9  1|4|6 |          7    3|6|9  1|3|4|6 |  3|6|8      2    3|4|8
------------------------+------------------------------+-----------------------
    2|4|9  3|4|9      8 |    1|2|3|9    2|3|7    2|3|7 |      5  1|3|7        6
    2|6|9      1    2|6 |    2|3|5|9        4  2|3|5|7 |    3|9      8  2|3|7|9
        7    3|9      5 |  1|2|3|6|9        8    2|3|6 |      4    1|3    2|3|9
------------------------+------------------------------+-----------------------
  1|2|3|4      5  1|2|4 |    2|3|4|6  2|3|6|7        9 |  1|3|8    3|7    3|7|8
        8      6      9 |        3|5        1    3|5|7 |      2      4    3|5|7
  1|2|3|4      7  1|2|4 |    2|3|4|5      2|3        8 |  1|3|9      6    3|5|9


If my notes are correct then those cells could be filled with 2, 9, 3, & 5, respectively (without looking at the effects of other cells).

True but irrelevant. The pattern depends only upon the positions of the 7s.

Question 1: Why is it an x-wing of 7's?

The following solver extract should help you to see why.

Code: Select all

1. Consider the chain r5c9-7-r5c6~7~r8c6-7-r8c9.
The cell r8c9 must contain the value 7 if the cell r5c9 doesn't.
Therefore, these two cells are the only candidates for the value 7 in Column 9.
- The move r7c9:=7 has been eliminated.
The values 2, 5, 7 and 9 occupy the cells r5c9, r6c9, r8c9 and r9c9 in some order.
- The moves r5c9:=3, r6c9:=3, r8c9:=3 and r9c9:=3 have been eliminated.
The value 3 in Box 8 must lie in Row 8.
- The moves r7c4:=3, r7c5:=3, r9c4:=3 and r9c5:=3 have been eliminated.
The value 2 is the only candidate for the cell r9c5.
2. Consider the chain r5c6-7-r5c9-7-r8c9-7-r8c6.
The cell r8c6 must contain the value 7 if the cell r5c6 doesn't.
Therefore, these two cells are the only candidates for the value 7 in Column 6.
- The move r4c6:=7 has been eliminated.
The values 5 and 7 occupy the cells r5c6 and r8c6 in some order.
- The moves r5c6:=2, r5c6:=3 and r8c6:=3 have been eliminated.
The cell r8c4 is the only candidate for the value 3 in Row 8.


Question 2: Is it also an x-wing of 3's?

No. The chain logic doesn't hold because there are many 3s in Columns 6 and 9.

[ExpertNovice]

True but irrelevant. The pattern depends only upon the positions of the 7s.

Arrggghhhh. (bear with me. I tend to make joke 90%)

No. The chain logic doesn't hold because there are many 3s in Columns 6 and 9.

Is it then reasonable to say that another "rule" to finding an x-wing is that when the x-wing spans four boxes the value may not be listed as a candidate outside those four boxes at least on the same row or column as the cells forming the x-wing.

Stated another way: r58c69 forms an x-wing for the value 7 because 7 does not appear as candidates in boxes 1,2,3,4, or 7 on rows 5, 8, 6, or 9.

If my suggested rule is correct then simply seeing that r1c9 has 3 listed as a candidate is enough to eliminate r58c69 from being considered as an x-wing for the value 3.

This makes sense and seems to be supported in many examples. However, an example at http://www.jibble.org/M4SuDoku/ would indicate then when the x-wing spans only two boxes then the value may appear in cells outside the boxes containing the x-wing. The suggested x-wing was r78c29. Yet the value also existed at r5c9 (same column different box).

Thanks for responding. I'm working through your solver extract now and will resist the urge to respond to the extract until I've worked through them fully.

[Shazbot]

Hi ExpertNovice,

take a look at Angus J and SadMan Sudoku to learn about and see examples of xwings.

If two rows have the same candidate only twice, and they're both in the same columns (the 4 form a perfect rectangle), then that candidate can be eliminated from other cells in the same columns. Or you can switch it by looking for two COLUMNS that contain the candidates only twice, and in the same rows, then remove that candidate from other cells in the same rows.

[emm]

ExpertNovice, the example in your link is not an Xwing, there are too many 5s in column 9.

Xwings have only 2 possibilities for the number in the row or column - it doesn't matter how many boxes it covers.

I wouldn't waste time on that link, except maybe to have a laugh at the big grid - it's an invalid, multi-solutioned puzzle with erroneous advice.

Why not go to a reputable site and get unlimited, properly-made puzzles with accurate hints. Click on the blue words for

1. The Pappocom programme
2. A long list of places to get puzzles at the bottom of the SadMan web page
3. Puzzles and user-friendly tips from Simple Sudoku

[tso]

There are only (two cells) in ROW 3 and 4 that can contain a 1, and they all reside in the same two COLUMNS. They therefore form an X-wing, excluding other 1's in their two COLUMNS.

There are only [two cells] in COLUMN 4 and 6 that can contain a 1, and they all reside in the same two ROWS. They therefore form an X-wing, excluding other 1's in their two ROWS.

Either X-wing excludes 1's from both r6c3 and r6c6.

Code: Select all

 . . . | . . . | . . .
 . . . | . . . | . . .
 . .(1)| . . . |(1). .
-------+-------+-------
 . .(1)| . . . |(1). .
 . . . | . . . | . . .
 . . 1 |[1].[1]| 1 . .
-------+-------+-------
 . . . |[1].[1]| . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

The following are similar to, but do not quite fit the definition of, x-wings. (Some call them "skewed x-wings" or "fishy cycles", though fishy cycles are not limited to just four cells.)

In each case,
"1" marks where 1s can go,
"a" marks cells that you know do not contain 1s, and
"x" marks cells where you can exclude 1s from.

If these are the only spots in ROW 2 and 3 where a 1 can go ...

Code: Select all

 x x x | . . . | x x x
 a a 1 | a a a | a 1 a
 a a 1 | a a a | 1 a a
-------+-------+-------
 . . x | . . . | . . .
 . . x | . . . | . . .
 . . x | . . . | . . .
-------+-------+-------
 . . x | . . . | . . .
 . . x | . . . | . . .
 . . x | . . . | . . .

... you may exclude 1s from the rest of box 1, box 3 and column 3

If these are the only spots in ROW 2 and 3 where a 1 can go ...

Code: Select all

 x x x | . . . | x x x
 1 a a | a a a | a 1 a
 a a 1 | a a a | 1 a a 
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

... then you may exclude 1s from the rest of boxes 1 and 3.


If these are the only spots in BOX 1 and 3 where a 1 can go ...

Code: Select all

 a a a | . . . | a a a
 1 a a | x x x | a 1 a
 a a 1 | x x x | 1 a a
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

... then you may exclude 1s from the rest of ROWS 2 and 3.

[ExpertNovice]

Tso,

Your example is the clearest example of x-wing formations I have seen.

Thanks for the bonus lesson! I do not recognize having seen this pattern before but they all make sense.

Hi ExpertNovice,

take a look at Angus J and SadMan Sudoku to learn about and see examples of xwings.

Shazbot, SadMan’s site was the first site I read and was what formed my knowledge of x-wings. It addresses the most basic form of the x-wing. As such it was very helpful.

Thanks for the Angus J site. It helps confirm my thoughts in the second post with the modification that candidates may exist on the same row or column but not both even within the same box.

ExpertNovice, the example in your link is not an Xwing, there are too many 5s in column 9.

Thanks, I was hoping they had incorrectly applied the x-wing. Had it been correct I would still be scratching my head!

As for why it was included. Well, contrived examples are nice but don't always show the complexities. Plus, if it had been correctly applied it would have shown a new complexity in x-wings that would be important in solving complex soduko puzzles.



Thanks to all who responded. Hopefully, it will help other novices.

[ronk]

If these are the only spots in ROW 2 and 3 where a 1 can go ...

Code: Select all

 x x x | . . . | x x x
 1 a a | a a a | a 1 a
 a a 1 | a a a | 1 a a 
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

If these are the only spots in BOX 1 and 3 where a 1 can go ...

Code: Select all

 a a a | . . . | a a a
 1 a a | x x x | a 1 a
 a a 1 | x x x | 1 a a
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

The same eliminations may be made even when several 1s exist in both rows 2 and 3 of both boxes 1 and 3.