Simple XY Chain

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Simple XY Chain

Postby Jasper32 » Mon Jun 30, 2008 7:29 pm

This should be a simple xy chain and most of the time I do this, it works. This time it doesn't work. My question is what did I do wrong or where is my thinking off. Your help will be appreciated. Many thanks.

A=1 b=7 c=1 then 1 should be eliminated from x but that doesn't work.


Code: Select all
 
 
 *-----------------------------------------------------------*
 | 8     35    4     | 9     2     35    | 16    16    7     |
 | 9     6     37    | 1     8     37    | 5     4     2     |
 | 1     57    2     | 4     6     57    | 9     3     8     |
 |-------------------+-------------------+-------------------|
 | 367   9     x136   | 5     4     2     | 1367  8     a16    |
 | 57    8     c15    | 3     9     6     | b17    2     4     |
 | 236   4     36    | 7     1     8     | 36    9     5     |
 |-------------------+-------------------+-------------------|
 | 256   125   8     | 26    7     9     | 4     156   3     |
 | 36    13    9     | 8     5     4     | 2     7     16    |
 | 4     257   567   | 26    3     1     | 8     56    9     |
 *-----------------------------------------------------------*
[/code]
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Postby daj95376 » Mon Jun 30, 2008 8:16 pm

I always start an XY-Chain with the assumption that a value is not true in a cell. Then, I search for a cell where that value is true.

Starting and ending with an assumption of true is faulty logic.
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Postby storm_norm » Mon Jun 30, 2008 9:06 pm

1... you could spot useless xy-wings ( which are xy-chains ) and try and extend them

2... always make sure the cells you are trying to string together are bi-value (contain only two candidates).

3...each end of the chain, when given a value, will be true in both directions for that value... this gives the ends of the chain a "pincer" characteristic... the same as a xy-wing (which is a xy-chain).

in other words, its true in both directions and the same value is true on each end, therefore any candidates those two ends see must be false.

AB---BC---CD---DA
A(B---B)(C---C)(D---D)A.,.,.,.,.four cell xy-chain, obviously there can be longer chains.

here is the xy-wing
AB---BC---CA
A(B---B)(C---C)A

so as you string together xy-chains, the value that you didn't use in the previous cell must occupy the next cell that it "sees".

for example... hypothetical situaion...
start with {1,2} then you would look for a bi-value cell that this cell can see containing either a 1 or a 2.. eg... {2,3}...since you used the 2 to connect them, you must use the 3 to connect the next bi-value cell...{3,4}... then use the 4...{4,1}... the 1 in this last cell as well as the 1 in the first cell would act like pincers and eliminate any other 1's they see. obviously all of the xy-chain cells must "see" the next cell in the chain to work.
(12)-(23)-(34)-(41)
1(2---2)(3---3)(4---4)1

notice how the 1's are left out, creating the "true" on each end characteristic regardless of the direction you travel through the chain.

visual example...

Image
3(4-----4)(9-----9)(1-----1)3

the 3's are left out A.K.A. true on each end and eliminates the 3's they see.

(3=4)r7c2-(4=9)r5c2-(9=1)r5c3-(1=3)r4c3; r79c1<>3
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Postby Glyn » Mon Jun 30, 2008 10:11 pm

Jasper32 You have a naked single r6c1=2 and 5's locked in column 2 of box 1, taking you to here.
Code: Select all
.---------------.---------------.---------------.
| 8    35   4   | 9    2    35  | 16   16   7   |
| 9    6    37  | 1    8    37  | 5    4    2   |
| 1    57   2   | 4    6    57  | 9    3    8   |
:---------------+---------------+---------------:
| 367  9    136 | 5    4    2   | 1367 8    16  |
| 57   8    15  | 3    9    6   | 17   2    4   |
| 2    4    36  | 7    1    8   | 36   9    5   |
:---------------+---------------+---------------:
| 56   12   8   | 26   7    9   | 4    156  3   |
| 36   13   9   | 8    5    4   | 2    7    16  |
| 4    27   567 | 26   3    1   | 8    56   9   |
'---------------'---------------'---------------'

This chain (5=6)r7c1-(6)r8c1=(6)r8c9-(6=5)r9c8 => r7c8,r9c3<>5 does the necessary.
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Postby daj95376 » Mon Jun 30, 2008 11:31 pm

Glyn wrote:This chain (5=6)r7c1-(6)r8c1=(6)r8c9-(6=5)r9c8 => r7c8,r9c3<>5 does the necessary.

It might have been more helpful to Jasper32 if you'd used an XY-Chain instead of a W-Wing:

Code: Select all
5-[r7c1]-6-[r8c1]-3-[r8c2]-1-[r8c9]-6-[r9c8]-5  =>  [r7c8],[r9c3]<>5
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Postby Glyn » Tue Jul 01, 2008 2:21 am

Thanks daj95376 I am not always aware of the terminology and I have just seen there was a short debate in the last week. or two. The chain I gave is not restricting itself to full use of the bivalue cells, am I right in thinking that is the distinction between the two forms?
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Postby daj95376 » Tue Jul 01, 2008 6:26 am

Glyn wrote:Thanks daj95376 I am not always aware of the terminology and I have just seen there was a short debate in the last week. or two. The chain I gave is not restricting itself to full use of the bivalue cells, am I right in thinking that is the distinction between the two forms?

Hello Glyn. Yes, an XY-Chain uses both values in the bivalue cells. It's an AIC where the strong inference (*) is within a bivalue cell, and the weak inference is between two bivalue cells.

Code: Select all
**********        **********        **********
5-[r7c1]-6-[r8c1]-3-[r8c2]-1-[r8c9]-6-[r9c8]-5  =>  [r7c8],[r9c3]<>5
         **********        **********
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