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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sun Jun 05, 2011 4:09 pm Post subject: Puzzle 11/06/05: ~ XY |
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| Code: | +-----------------------+
| 8 . 6 | 4 . 9 | . . . |
| . 5 . | 6 . . | . . . |
| 2 . 7 | . . . | . . . |
|-------+-------+-------|
| . 9 . | 5 . . | . . . |
| . . . | 9 7 . | 1 . . |
| 1 . . | 8 . 3 | . 7 . |
|-------+-------+-------|
| 9 . . | . 6 . | 8 . 7 |
| . . . | . . 8 | . 1 . |
| . . . | . . . | 6 . 5 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jun 06, 2011 2:49 pm Post subject: |
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I stumbled into a nice chain while looking for xy-wings............
(3=4)r9c1-(4=1)r9c6-r3c6=(1-3)r3c4=(3)r123c5; r9c5<>3=9
Ted |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Mon Jun 06, 2011 3:58 pm Post subject: |
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An alternative to Ted's chain (which to me looks like an m-wing with a r9 3=1) is this xy-chain...
| Quote: | | (1=3)r3c4 - (3=4)r3c2 - (4=3)r2c1 - (3=4)r9c1 - (4=1)r9c6 ; r3c6<>1, r79c4<>1 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jun 06, 2011 5:32 pm Post subject: |
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| Code: | after basics
+--------------------------------------------------------------------------------+
| 8 1 6 | 4 235 9 | 7 235 23 |
| 34 5 9 | 6 238 7 | 234 2348 1 |
| 2 34 7 | 13 358 15 | 3459 345689 34689 |
|--------------------------+--------------------------+--------------------------|
| 7 9 348 | 5 1 26 | 234 23468 23468 |
| 56 348 348 | 9 7 26 | 1 234568 23468 |
| 1 26 25 | 8 4 3 | 59 7 69 |
|--------------------------+--------------------------+--------------------------|
| 9 234 12345 | 123 6 145 | 8 234 7 |
| 56 23467 2345 | 237 359 8 | 2349 1 2349 |
| 34 23478 12348 | 1237 39 14 | 6 2349 5 |
+--------------------------------------------------------------------------------+
# 109 eliminations remain
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This puzzle is interesting because it only has a single XY-Chain, which cracks the puzzle (as peterj discovered).
It also has 2x (nearly identical) M-Wing that crack the puzzle:
| Code: | M-Wing 2B: (1=5)r3c6 - r7c6 = (5-1)r7c3 = (1)r9c3 => r9c6<>1
M-Wing 3B: (1=5)r3c6 - r7c6 = (5-1)r7c3 = (1)r7c46 => r9c6<>1
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After that, an extraneous XYZ-Wing still needs a chain to crack the puzzle (like Ted used). |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jun 07, 2011 4:33 am Post subject: |
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| The XY-Chain is also what I call an XY-Wing Chain or what others call an Extended XY-Wing, 13-34-34-34-14, where the three 34 cells act as the one pivot cell in an XY-Wing. |
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