XY Chain....revisited

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XY Chain....revisited

Postby Jasper32 » Tue Aug 26, 2008 4:32 pm

It seems like everytime I think I have the XY chain down pat, something comes along I don't understand. It the puzzle below, please look at

r9c4=2 r4c4=6 r4c9=1 r9c9=2

If I go backwards it still looks like as if r9c4 or r9c2 should equal 2 and I could eliminate 2 from r9c7.

I would appreciate somebody informing me of my faulty logic by explaning in detail where I went wrong.

Thank you,


Code: Select all


 *-----------*
 |.5.|.1.|.7.|
 |91.|7.8|53.|
 |.87|4.5|.1.|
 |---+---+---|
 |593|.4.|78.|
 |...|873|.95|
 |.78|.5.|.23|
 |---+---+---|
 |..5|1.7|96.|
 |..1|5..|.47|
 |769|.84|.5.|
 *-----------*

 
 *--------------------------------------------------------------------*
 | 2346   5      246    | 2369   1      269    | 268    7      24689  |
 | 9      1      246    | 7      26     8      | 5      3      246    |
 | 236    8      7      | 4      2369   5      | 26     1      269    |
 |----------------------+----------------------+----------------------|
 | 5      9      3      | 26     4      126    | 7      8      16     |
 | 1246   24     246    | 8      7      3      | 146    9      5      |
 | 146    7      8      | 69     5      169    | 146    2      3      |
 |----------------------+----------------------+----------------------|
 | 248    234    5      | 1      23     7      | 9      6      28     |
 | 28     23     1      | 5      69     69     | 238    4      7      |
 | 7      6      9      | 23     8      4      | 123    5      12     |
 *--------------------------------------------------------------------*


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Postby RW » Tue Aug 26, 2008 5:29 pm

Your chain says that if r9c4=2 then r9c9=2. Notice anything odd here? What's the elimination?

RW
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Postby Glyn » Tue Aug 26, 2008 5:56 pm

Jasper32 If you still can't work it out from RW's tip.

Select here for an extra clue to what RW wrote:You have proved that if r9c4=2 then r9c4<>2. A contradiction leading to r9c4<>2.
Your chain contains the XY-wing based on r4c9 which yields the same elimination.
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Re: XY Chain....revisited

Postby daj95376 » Tue Aug 26, 2008 8:10 pm

Jasper32 wrote:I would appreciate somebody informing me of my faulty logic by explaning in detail where I went wrong.

It's the same problem you've had previously. You want to start with an assertion ... and XY-Chains start with a negation.

This seems to be a problem for numerous people. So you are not alone.

Use Glyn's concealed comment to find a 3-cell XY-Chain.
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Re: XY Chain....revisited

Postby Luke » Thu Aug 28, 2008 11:56 am

Jasper32 wrote:It seems like everytime I think I have the XY chain down pat, something comes along I don't understand. It the puzzle below, please look at

r9c4=2 r4c4=6 r4c9=1 r9c9=2

If I go backwards it still looks like as if r9c4 or r9c2 should equal 2 and I could eliminate 2 from r9c7.

I would appreciate somebody informing me of my faulty logic by explaning in detail where I went wrong.

Code: Select all
 
 *--------------------------------------------------------------------*
 | 2346   5      246    | 2369   1      269    | 268    7      24689  |
 | 9      1      246    | 7      26     8      | 5      3      246    |
 | 236    8      7      | 4      2369   5      | 26     1      269    |
 |----------------------+----------------------+----------------------|
 | 5      9      3      | 26     4      126    | 7      8      16     |
 | 1246   24     246    | 8      7      3      | 146    9      5      |
 | 146    7      8      | 69     5      169    | 146    2      3      |
 |----------------------+----------------------+----------------------|
 | 248    234    5      | 1      23     7      | 9      6      28     |
 | 28     23     1      | 5      69     69     | 238    4      7      |
 | 7      6      9      | 23     8      4      | 123    5      12     |
 *--------------------------------------------------------------------*

Try the "Left Over Method" described back in Feb in this thread, and you'll never have this problem again.

If you start with the 2 in r9c4, then the 3 is the "left over" number. In your example you could say, "3 is left over and
2 can see 2, (in r4c4)
6 can see 6, (in r4c9)
1 can see 1, (in r9c9)
and 2 is left over."

It's not an XY cycle if the first and last "left over" numbers are not the same, simple as that. When they *are* the same, any value that both the "left over" values can see is the elimination.

Looking at Glyn's example, you would start with r4c4, and the 2 would be the "left over" number. You could say, "2 is left over and
6 can see 6,
1 can see 1,
and 2 is left over."

Both "left over" numbers are 2, and both can see the 2 in r9c4, and there ya have it.

Take a look at another XY chain from this puzzle and see if you can find two "left over" 6's.
Code: Select all
 
 *--------------------------------------------------------------------*
 | 2346   5      246    | 2369   1      269    | 268    7      24689  |
 | 9      1      246    | 7      *26    8      | 5      3      246    |
 | 236    8      7      | 4      2369   5      | 26     1      269    |
 |----------------------+----------------------+----------------------|
 | 5      9      3      | *26    4      126    | 7      8      16     |
 | 1246   24     246    | 8      7      3      | 146    9      5      |
 | 146    7      8      | 69     5      169    | 146    2      3      |
 |----------------------+----------------------+----------------------|
 | 248    234    5      | 1      *23    7      | 9      6      28     |
 | 28     23     1      | 5      69     69     | 238    4      7      |
 | 7      6      9      | *23    8      4      | 123    5      12     |
 *--------------------------------------------------------------------*
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Xy Chain .... revisited

Postby Jasper32 » Sat Aug 30, 2008 9:01 pm

I want to thank all of you for your replies and your enduring patience. I truly now think I fully grasp the concept of the XY chain. A special thanks to Luke 451 for his enlightment on this subject.

Now if anyone has a way of rapidly finding ALS's, I would love tp hear from you.

Again, thanks to all of you who replied.

Jasper
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Re: Xy Chain .... revisited

Postby DonM » Sun Aug 31, 2008 12:20 am

Jasper32 wrote:Now if anyone has a way of rapidly finding ALS's, I would love to hear from you.


Jasper, this may help:

http://www.sudoku.org.uk/SudokuThread.asp?fid=4&sid=10326&p1=1&p2=11
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