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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Sun Nov 01, 2009 5:36 am Post subject: XY-Loop |
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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 |
+---------+--------+-------------+
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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.
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| Posted: Sun Nov 01, 2009 6:50 am Post subject: |
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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.  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Nov 01, 2009 4:35 pm Post subject: |
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| Quote: | | The one you have shown has all other eliminations already done. |
Thanks! Maybe that's why I couldn't find anything to eliminate.  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Nov 02, 2009 1:53 am Post subject: |
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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 |
+-----------------------+
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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: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Nov 02, 2009 3:12 am Post subject: |
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This gets wild quickly!  | 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: 5770
Location: Rochester, NY, USA
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| Posted: Mon Nov 02, 2009 5:51 am Post subject: |
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| 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
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| Posted: Fri May 14, 2010 1:48 am Post subject: |
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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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