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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Mon Oct 20, 2008 2:24 am Post subject: Oct 20 VH |
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Two x-wings appear early. You need use only one of them, then an xy-wing will finish the puzzle.
Earl |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Oct 20, 2008 3:53 am Post subject: |
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Alternate solution. After basics:
| Code: |
+----------+-------------+-----------+
| 17 5 2 | 789 16 789 | 3 4 68 |
| 3 9 67 | 5 4 78 | 68 1 2 |
| 14 8 46 | 3 16 2 | 5 7 9 |
+----------+-------------+-----------+
| 2 4 8 | 69 7 69 | 1 3 5 |
| 9 6 3 | 1 8 5 | 7 2 4 |
| 5 7 1 | 4 2 3 | 9 68 68 |
+----------+-------------+-----------+
| 48 2 5 | 68 3 1 | 468 9 7 |
| 6 3 47 | 2 9 478 | 48 5 1 |
| 478 1 9 | 678 5 4678 | 2 68 3 |
+----------+-------------+-----------+
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Play this puzzle online at the Daily Sudoku site
| Quote: | | M-Wing on 48 in boxes 79 takes out the 8 from r9c8 which solves the puzzle |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Oct 20, 2008 6:06 am Post subject: |
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| x-wing and a bug+1 |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Mon Oct 20, 2008 6:55 am Post subject: |
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1 x-wing opens up an xy-wing, and the puzzle is solved. Is there an alternate solution?
| Marty R. wrote: | Alternate solution. After basics:
| Code: |
+----------+-------------+-----------+
| 17 5 2 | 789 16 789 | 3 4 68 |
| 3 9 67 | 5 4 78 | 68 1 2 |
| 14 8 46 | 3 16 2 | 5 7 9 |
+----------+-------------+-----------+
| 2 4 8 | 69 7 69 | 1 3 5 |
| 9 6 3 | 1 8 5 | 7 2 4 |
| 5 7 1 | 4 2 3 | 9 68 68 |
+----------+-------------+-----------+
| 48 2 5 | 68 3 1 | 468 9 7 |
| 6 3 47 | 2 9 478 | 48 5 1 |
| 478 1 9 | 678 5 4678 | 2 68 3 |
+----------+-------------+-----------+
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Play this puzzle online at the Daily Sudoku site
| Quote: | | M-Wing on 48 in boxes 79 takes out the 8 from r9c8 which solves the puzzle |
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Mon Oct 20, 2008 8:02 am Post subject: w wing is an alternative! |
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| The W wing on 68 in boxes 8 and 9 operating on either the 8s in row 8 or col1 solves it immediately |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Oct 20, 2008 10:05 am Post subject: |
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Reverse the starting and ending (48) in Marty's solution:
| Code: | M-Wing on 48 in boxes 79 takes out the 8 from r7c4 which solves the puzzle
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Oct 20, 2008 11:41 am Post subject: |
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| daj95376 wrote: | Reverse the starting and ending (48) in Marty's solution:
| Code: | M-Wing on 48 in boxes 79 takes out the 8 from r7c4 which solves the puzzle
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m-wing is my downfall. I can never see them.
Is this the correct logic?
r7c1=8 => r7c4<>8
r7c1=4 r8c7=4 r8c8=7 r8c6=8 => r7c4<>8 |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon Oct 20, 2008 1:25 pm Post subject: |
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| Same thing - x-wings and the xy. Though I didn't see any bug+1 before these steps. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Oct 20, 2008 2:12 pm Post subject: |
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| cgordon wrote: | | Same thing - x-wings and the xy. Though I didn't see any bug+1 before these steps. |
I found the bug here after the x-wing and some basics: | Code: |
*--------------------------------------------------*
| 17 5 2 | 78 16 9 | 3 4 68 |
| 3 9 67 | 5 4 78 | 68 1 2 |
| 14 8 46 | 3 16 2 | 5 7 9 |
|----------------+----------------+----------------|
| 2 4 8 | 9 7 6 | 1 3 5 |
| 9 6 3 | 1 8 5 | 7 2 4 |
| 5 7 1 | 4 2 3 | 9 68 68 |
|----------------+----------------+----------------|
| 48 2 5 | 68 3 1 | 46 9 7 |
| 6 3 47 | 2 9 78 | 48 5 1 |
| 78 1 9 | 678 5 4 | 2 68 3 |
*--------------------------------------------------* |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Oct 20, 2008 2:20 pm Post subject: |
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I did not check to determine exactly what was useful, but I had a x-wing on <7> and then on <8>, followed by the BUG+1 that makes r9c4=8.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Oct 20, 2008 3:47 pm Post subject: |
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| Quote: | Is this the correct logic?
r7c1=8 => r7c4<8> r7c4<>8 |
As I understand them, the two 48 cells are connected by two strong links on 4. Then the 8 in r7c1 is extended to r9c1, acting as a pincer with r8c7.
Have you seen Keith's third post in this thread?
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Oct 20, 2008 5:28 pm Post subject: |
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| arkietech wrote: | m-wing is my downfall. I can never see them.
Is this the correct logic?
r7c1=8 => r7c4<>8
r7c1=4 r8c7=4 r8c8=7 r8c6=8 => r7c4<>8 |
Not quite. The solution for an M-Wing should only use the candidate values in the bivalue cells. Your solution includes a (7) value. Maybe this will help.
Notice the (*) cells form an L pattern in strong links for (4) joining the (48) cells. Now, notice the strong links in (8) -- (a) for my solution and (b) for Marty's solution. They each include one end of the "L" pattern. At this point, a standard chain format exists for any M-Wing.
| Code: | (a) 8-[r7c1]-4-[r7c7]=4=[r8c7]=8=[r8c6] => [r7c4]<>8 (for my solution)
(b) 8-[r8c7]-4-[r7c7]=4=[r7c1]=8=[r9c1] => [r9c8]<>8 (for Marty's solution)
|----------------------+----------------------+----------------------|
| *48b 2 5 | 68 3 1 | *468 9 7 |
| 6 3 47 | 2 9 478a | *48a 5 1 |
| 478b 1 9 | 678 5 4678 | 2 68 3 |
+--------------------------------------------------------------------+
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If you are comfortable with the use of strong/weak inference, then you'll notice that both instances of weak inference are satisfied by a strong link. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Oct 20, 2008 7:28 pm Post subject: |
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daj95376 said: | Code: | (a) 8-[r7c1]-4-[r7c7]=4=[r8c7]=8=[r8c6] => [r7c4]<>8 (for my solution)
(b) 8-[r8c7]-4-[r7c7]=4=[r7c1]=8=[r9c1] => [r9c8]<>8 (for Marty's solution)
|----------------------+----------------------+----------------------|
| *48b 2 5 | 68 3 1 | *468 9 7 |
| 6 3 47 | 2 9 478a | *48a 5 1 |
| 478b 1 9 | 678 5 4678 | 2 68 3 |
+--------------------------------------------------------------------+
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I finally see it! What about
(c) 8-[r7c1]-4-[r7c7]=4=[r8c7]=8=[r9c8] => [r7c4]<>8 ?
oops! r9c8 is weak wrong again.
Thanks for the help |
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lg161
Joined: 17 Oct 2006
Posts: 12
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| Posted: Mon Oct 20, 2008 9:24 pm Post subject: oct 20 vh |
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| I am at Marty's position. What are the 2 x-wings and 1 xy-wing that solve it? ty. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Oct 20, 2008 10:29 pm Post subject: Re: oct 20 vh |
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| lg161 wrote: | | I am at Marty's position. What are the 2 x-wings and 1 xy-wing that solve it? ty. |
Your question doesn't have a simple answer because various combinations of X-Wings and XY-Wings solve the puzzle from Marty's PM.
This is the most efficient.
| Code: | r28 X-Wing <> 8 [r19c6],[r7c7]
XY-Wing [r7c7]/[r7c1]+[r9c8] <> 8 [r9c1] -or-
XY-Wing [r7c7]/[r7c4]+[r8c7] <> 8 [r8c6]
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This allows more XY-Wing choices.
| Code: | c14 X-Wing <> 7 [r19c6] -or-
r28 X-Wing <> 7 [r19c6]
r28 X-Wing <> 8 [r19c6],[r7c7]
Naked Singles
XY-Wing [r7c7]/[r7c1]+[r9c8] <> 8 [r9c1] -or-
XY-Wing [r7c7]/[r7c4]+[r8c7] <> 8 [r8c6] -or-
XY-Wing [r8c3]/[r7c1]+[r8c6] <> 8 [r7c4] -or-
XY-Wing [r8c3]/[r8c7]+[r9c1] <> 8 [r9c8]
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Wendy W
Joined: 04 Feb 2008
Posts: 144
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| Posted: Mon Oct 20, 2008 11:45 pm Post subject: |
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| Basics and a couple of skyscrapers did it for me quickly, and thank goodness for that! All those 6-8s were making me dizzy. |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Tue Oct 21, 2008 3:20 am Post subject: Re: oct 20 vh |
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| lg161 wrote: | | I am at Marty's position. What are the 2 x-wings and 1 xy-wing that solve it? ty. |
I solved it with an x-wing of 8s on rows 2 & 8. This removes three 8s, the most important one is in row 7, col 7.
| Code: |
+----------+-------------+-----------+
| 17 5 2 | 789 16 789 | 3 4 68 |
| 3 9 67 | 5 4 78 | 68 1 2 |
| 14 8 46 | 3 16 2 | 5 7 9 |
+----------+-------------+-----------+
| 2 4 8 | 69 7 69 | 1 3 5 |
| 9 6 3 | 1 8 5 | 7 2 4 |
| 5 7 1 | 4 2 3 | 9 68 68 |
+----------+-------------+-----------+
| 48 2 5 | 68 3 1 | 468 9 7 |
| 6 3 47 | 2 9 478 | 48 5 1 |
| 478 1 9 | 678 5 4678 | 2 68 3 |
+----------+-------------+-----------+
|
Play this puzzle online at the Daily Sudoku site
As you can see below, after removing the 8s, a 46 is left in Row 7, col 7. This 46 is a pivot for an xy wing of 68-46-48. This allows removal of an 8 in col 6, row 8. (478 becomes 47). It is easy to solve from here.
| Code: |
+----------+------------+----------+
| 17 5 2 | 789 16 79 | 3 4 68 |
| 3 9 67 | 5 4 78 | 68 1 2 |
| 14 8 46 | 3 16 2 | 5 7 9 |
+----------+------------+----------+
| 2 4 8 | 69 7 69 | 1 3 5 |
| 9 6 3 | 1 8 5 | 7 2 4 |
| 5 7 1 | 4 2 3 | 9 68 68 |
+----------+------------+----------+
| 48 2 5 | 68 3 1 | 46 9 7 |
| 6 3 47 | 2 9 478 | 48 5 1 |
| 478 1 9 | 678 5 467 | 2 68 3 |
+----------+------------+----------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Oct 21, 2008 6:58 am Post subject: |
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| Quote: | | ... m-wing is my downfall. I can never see them. |
Let me try to summarize the basic idea. Suppose you have two cells that have the same two candidates, XY.
1. They may be a pair, in which case any cells that sees both of them cannot be X or Y. (aka a "naked pair". The two cells are both in the same row, column, or block.)
2. They may be unconnected, in which case you can do nothing.
3. They may be a remote pair. Any cell that sees both cannot be X or Y.
4. They may be a complementary pair. They have the same value, be it X or Y.
5. They may be a W-wing. Any cell that sees both XY cells cannot be Y (or X).
To recap:
Remote pair: One is X, one is Y.
Complementary pair: Both are X, or both are Y.
W-wing: One, or both, are X. Or; one, or both, are Y.
In the remote pair and the W-wing, the XY cells are themselves the pincers. They can make eliminations in any cell that sees both of them.
The complementary pair needs something more to be useful. Suppose the cells are A and B, and that both are X. If we can find a strong link on Y from B to a third cell, C, we have an M-wing. The logic is this:
A is Y. Or;
A is X; B is X; C is Y.
Any cell that sees both A and C cannot be Y.
The basic idea is to find two cells that have the same two candidates, and then to figure out how they might be useful. To me, remote pairs, W-wings, and M-wings, should be in the same aisle of my grocery store.
Keith |
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