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XY-Loop

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Nov 01, 2009 5:36 am    Post subject: XY-Loop Reply with quote

I am having trouble grasping these. First, is my definition correct, that an XY-Loop is an XY-Chain whose start and end are in the same house? If that is true, then supposedly more eliminations can be made?

Consider this:

Code:

+---------+--------+-------------+
| 78 1 3  | 24 6 9 | 258 45  257 |
| 6  2 4  | 8  7 5 | 1   9   3   |
| 9  5 78 | 24 3 1 | 28  47  6   |
+---------+--------+-------------+
| 5  4 6  | 3  1 2 | 7   8   9   |
| 38 9 28 | 56 4 7 | 356 1   25  |
| 23 7 1  | 56 9 8 | 23  56  4   |
+---------+--------+-------------+
| 4  8 57 | 9  2 3 | 56  567 1   |
| 1  3 9  | 7  5 6 | 4   2   8   |
| 27 6 25 | 1  8 4 | 9   3   57  |
+---------+--------+-------------+

Play this puzzle online at the Daily Sudoku site

Start an XY-Chain with the 7 in r9c9, then the 2 in r9c1 and continue it for four more cells and you end up with a 5 in r5c9, taking out the 5 from r1c9. What, if any, are the other eliminations? I tried a couple more chains in other cells in the loop and nothing seemed to happen.

What's the next step after the original elimination of that 5?

(It looks like the W-Wing on 28 might finish the puzzle, but I'd like to get a handle on that loop before proceeding.)
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wapati



Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.

PostPosted: Sun Nov 01, 2009 6:50 am    Post subject: Reply with quote

You have the basic idea. To keep it easy use bi-value cells only.

It can be done with more but that is ALS, more properly.

If you build a chain and find that the endpoints are in a house that means that all the links are in a house for their digit.

You can build the chain starting anywhere and each time do a different digit elimination.

The one you have shown has all other eliminations already done. Smile
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sun Nov 01, 2009 4:35 pm    Post subject: Reply with quote

Quote:
The one you have shown has all other eliminations already done.

Thanks! Maybe that's why I couldn't find anything to eliminate. Very Happy
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Nov 02, 2009 1:53 am    Post subject: Reply with quote

Marty,

This puzzle is from Mike Barker's zoo contributions. You should have lots of fun finding all the eliminations for the XY-Loop.

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

Play this puzzle online at the Daily Sudoku site

Code:
 +--------------------------------------------------------------+
 |  1345  456   1459  |  139   139   8     |  1356  2     7     |
 |  123  *26    8     |  1239  7     5     |  4     1369 *36    |
 |  7    *25    1259  |  6     1239  4     |  8     139  *35    |
 |--------------------+--------------------+--------------------|
 |  1245  3     1245  |  8     1245  9     |  26    7     246   |
 |  124   8     7     |  1234  1234  6     |  9     5     234   |
 |  245   9     6     |  234   2345  7     |  23    8     1     |
 |--------------------+--------------------+--------------------|
 |  8     7     245   |  49    469   1     |  2356  36    2356  |
 |  9     245   245   |  7     46    3     |  1256  16    8     |
 |  6     1     3     |  5     8     2     |  7     4     9     |
 +--------------------------------------------------------------+
 # 84 eliminations remain
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arkietech



Joined: 31 Jul 2008
Posts: 1709
Location: Northwest Arkansas USA

PostPosted: Mon Nov 02, 2009 3:12 am    Post subject: Reply with quote

This gets wild quickly! Shocked
Code:
 +--------------------------------------------------------------+
 |  1345  456   1459  |  139   139   8     |  156-3 2     7     |
 |  13-2 *26    8     |  1239  7     5     |  4     19-36*36    |
 |  7    *25    19-25 |  6     23-19 4     |  8     19-3 *35    |
 |--------------------+--------------------+--------------------|
 |  1245  3     1245  |  8     1245  9     |  26    7     246   |
 |  124   8     7     |  1234  1234  6     |  9     5     24-3  |
 |  245   9     6     |  234   2345  7     |  23    8     1     |
 |--------------------+--------------------+--------------------|
 |  8     7     245   |  49    469   1     |  2356  36    256-3 |
 |  9     45-2  245   |  7     46    3     |  1256  6-1   8     |
 |  6     1     3     |  5     8     2     |  7     4     9     |
 +--------------------------------------------------------------+
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Mon Nov 02, 2009 5:51 am    Post subject: Reply with quote

Quote:
This puzzle is from Mike Barker's zoo contributions. You should have lots of fun finding all the eliminations for the XY-Loop.

Thanks Danny. I think I exploited the loop to the fullest, based on the eliminations that Dan shows in his grid.

Of course, had I done the puzzle without knowing about the loop, I probably wouldn't have looked for or found it, but that's another story. But it was a good exercise.
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Fri May 14, 2010 1:48 am    Post subject: Reply with quote

Hi Marty,
Another way to look at this xy loop is that it is a multidigit xy-chain. It is an xy-chain for each of the digits in the loop, 2,3,5.and 7.
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