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Set XY_01 Puzzle 01

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu Mar 19, 2009 3:18 pm    Post subject: Set XY_01 Puzzle 01 Reply with quote
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Code:
 +-----------------------+
 | 6 . . | . . . | 2 . . |
 | . 4 . | . . 5 | 6 . . |
 | . . 3 | 1 . . | . . 7 |
 |-------+-------+-------|
 | . . 5 | . . 7 | . . . |
 | . . . | . 5 8 | . 6 4 |
 | . 9 . | 2 1 . | . . 5 |
 |-------+-------+-------|
 | 1 2 . | . . . | 4 9 . |
 | . . . | . 6 . | 3 . . |
 | . . 9 | . 4 2 | . . . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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gindaani



Joined: 06 Mar 2009
Posts: 79
PostPosted: Thu Mar 19, 2009 6:15 pm    Post subject: Reply with quote
I found this one fairly straight forward. Basics plus a sashimi x-wing, a finned x-wing, and some x-chains got me to here:

Code:

+----------+---------+------------+
| 6  15 78 | 4  78 9 | 2  15  3   |
| 27 4  12 | 78 3  5 | 6  18  9   |
| 9  58 3  | 1  2  6 | 58 4   7   |
+----------+---------+------------+
| 4  3  5  | 6  9  7 | 18 28  128 |
| 27 17 12 | 3  5  8 | 9  6   4   |
| 8  9  6  | 2  1  4 | 7  3   5   |
+----------+---------+------------+
| 1  2  78 | 5  78 3 | 4  9   6   |
| 5  78 4  | 9  6  1 | 3  27  28  |
| 3  6  9  | 78 4  2 | 15 578 18  |
+----------+---------+------------+

Play this puzzle online at the Daily Sudoku site

The final step was an xy-chain:

r9c9<>1 => r8c9=2 => r8c2=8 => r3c2=5 => r3c7=8 => r4c7=1
This eliminates 1 from r9c7 and r4c9, which solves the puzzle.

PS Is this the preferred notation for xy-chains?
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Thu Mar 19, 2009 8:30 pm    Post subject: Reply with quote
gindaani wrote:

Is this the preferred notation for xy-chains?


Hi gindanni, and welcome to our group. I am still trying to learn about notations, and will let the senior group members answer your question.

Not being a fan of chains (probably because I still am not good at finding them), it took me seven enjoyable VH steps to complete this puzzle as follows:
Quote:
a 4-cell Remote pair <78>,
a 6-cell Remote Pair <78>,
x-wing7,
sashimi x-wing8,
finned x-wing8,
xy-wing127 with a pseudo-cell pincer, and finally
xy-wing278 with both pincers transported.

I have no idea if any steps were unnecessary.
Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu Mar 19, 2009 8:50 pm    Post subject: Reply with quote
gindaani wrote:
The final step was an xy-chain:

r9c9<>1 => r8c9=2 => r8c2=8 => r3c2=5 => r3c7=8 => r4c7=1
This eliminates 1 from r9c7 and r4c9, which solves the puzzle.

PS Is this the preferred notation for xy-chains?

Welcome to the forum and this sub-forum!!!

Your XY-Chain is missing cell [r8c8], but you get the job done anyway. As for notation, may I suggest that you just mark your PM as follows.

Code:
 XY-Chain a-b-c-d-e-f-g => [r4c9],[r9c7]<>1
 +-----------------------------------------------------+
 |  6    15   78   |  4    78   9    |  2    15   3    |
 |  27   4    12   |  78   3    5    |  6    18   9    |
 |  9   e58   3    |  1    2    6    | f58   4    7    |
 |-----------------+-----------------+-----------------|
 |  4    3    5    |  6    9    7    | g18   28   128  |
 |  27   17   12   |  3    5    8    |  9    6    4    |
 |  8    9    6    |  2    1    4    |  7    3    5    |
 |-----------------+-----------------+-----------------|
 |  1    2    78   |  5    78   3    |  4    9    6    |
 |  5   d78   4    |  9    6    1    |  3   c27  b28   |
 |  3    6    9    |  78   4    2    |  15   578 a18   |
 +-----------------------------------------------------+
 # 27 eliminations remain
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gindaani



Joined: 06 Mar 2009
Posts: 79
PostPosted: Thu Mar 19, 2009 9:12 pm    Post subject: Reply with quote
Thanks for the suggestion on marking the PM. What is the easiest way to add the letters without messing up the alignment?

daj95376 wrote:
Your XY-Chain is missing cell [r8c8], but you get the job done anyway.


I thought [r8c8] was redundant since (8=8)r8c29. Anyway, I used a different path coming the other direction. That path is a little longer, but works in both directions:

Code:
 XY-Chain a-b-c-d-e-f-g-h => [r4c9],[r9c7]<>1
 +-----------------------------------------------------+
 |  6    15   78   |  4    78   9    |  2    15   3    |
 |  27   4    12   |  78   3    5    |  6    18   9    |
 |  9   f58   3    |  1    2    6    | g58   4    7    |
 |-----------------+-----------------+-----------------|
 |  4    3    5    |  6    9    7    | h18   28   128  |
 |  27   17   12   |  3    5    8    |  9    6    4    |
 |  8    9    6    |  2    1    4    |  7    3    5    |
 |-----------------+-----------------+-----------------|
 |  1    2   d78   |  5   c78   3    |  4    9    6    |
 |  5   e78   4    |  9    6    1    |  3    27   28   |
 |  3    6    9    | b78   4    2    |  15   578 a18   |
 +-----------------------------------------------------+
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
PostPosted: Thu Mar 19, 2009 9:50 pm    Post subject: Reply with quote
Code:
.------------.-----------.--------------.
| 6   15  78 | 4   78  9 | 2   15   3   |
| 27  4   12 | 78  3   5 | 6   18   9   |
| 9   58  3  | 1   2   6 | 58  4    7   |
:------------+-----------+--------------:
| 4   3   5  | 6   9   7 | 18  28   128 |
| 27  17  12 | 3   5   8 | 9   6    4   |
| 8   9   6  | 2   1   4 | 7   3    5   |
:------------+-----------+--------------:
| 1   2   78 | 5   78  3 | 4   9    6   |
| 5   78  4  | 9   6   1 | 3   27   28  |
| 3   6   9  | 78  4   2 | 15  578  18  |
'------------'-----------'--------------'


Here I saw only two cells with three candidates.
I have no idea whta this may be called but,
when I look at them as BUGs, they both want to be 8.
Set either to 8, they are both 8.

Works for me, and this puzzle, is there a name for this?

Yep, I see a 6 cell xy-chain and an x-chain on 8s that also work.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu Mar 19, 2009 11:42 pm    Post subject: Reply with quote
wapati wrote:
Here I saw only two cells with three candidates.
I have no idea whta this may be called but,
when I look at them as BUGs, they both want to be 8.
Set either to 8, they are both 8.

Works for me, and this puzzle, is there a name for this?

It's called a BUG+2 and it's the primary reason why I went ahead and posted this puzzle. It provides an alternative to finding XY-Chains.

There's also a Skyscraper in <8> that can be extended to the <18> cells found by gindaani. Another way to get around XY-Chains.

However, a short XY-Chain might be integral to the solution of some other puzzle.
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
PostPosted: Thu Mar 19, 2009 11:47 pm    Post subject: Reply with quote
daj95376 wrote:

It's called a BUG+2 and it's the primary reason why I went ahead and posted this puzzle.


If the two "BUGS" don't agree but there are only two 3 candidate cells, what is that called? (I have no idea).
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Mar 20, 2009 12:54 am    Post subject: Reply with quote
wapati wrote:
daj95376 wrote:

It's called a BUG+2 and it's the primary reason why I went ahead and posted this puzzle.


If the two "BUGS" don't agree but there are only two 3 candidate cells, what is that called? (I have no idea).

I'm not sure what you mean by agree. I'm limited in experience with BUGs. It's only recently that I've ventured past BUG+1. So, I'm probably not going to be much help in answering questions.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Fri Mar 20, 2009 1:02 am    Post subject: Reply with quote
Code:
.------------------.------------------.------------------.
| 6     1578  178  | 4     78    9    | 2    15-8   3    |
| 27    4     1278 | 78    3     5    | 6    1-8    9    |
| 9     58    3    | 1     2     6    |*58    4     7    |
:------------------+------------------+------------------:
| 4     3     5    | 6     9     7    |U18   *28   U128  |
| 27    17    127  | 3     5     8    | 9     6     4    |
| 8     9     6    | 2     1     4    | 7     3     5    |
:------------------+------------------+------------------:
| 1     2     78   | 5     78    3    | 4     9     6    |
| 5     78    4    | 9     6     1    | 3     278   28   |
| 3     6     9    | 78    4     2    |U158   578  U18   |
'------------------'------------------'------------------'

UR on {1,8} r49c79 says that neither the 2 in r4c9 nor the 5 in r9c7 can both be false
gives us this strong inference... UR18[(2)r4c9 = (5)r9c7]
extends to this chain...
(8=2)r4c8 - UR18[(2)r4c9 = (5)r9c7] - (5=8)r3c7; r12c8 <> 8

when the dust settles, the type 1 UR on {2,8} finishes it.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri Mar 20, 2009 3:41 pm    Post subject: Reply with quote
I used the Remote Pairs on 78, two X-Wings, 2 and 1, Hidden UR on 18 and the Type 1 UR on 28.
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