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Sept 27 vh

 
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crunched



Joined: 05 Feb 2008
Posts: 168

PostPosted: Sat Sep 27, 2008 7:34 am    Post subject: Sept 27 vh Reply with quote

I tried this 3 times and solved it 3 different ways. I found 2 x wings and 2 xy wings.

Code:

+-------------+----------+---------------+
| 678 3   1   | 2  4 58  | 5678 678  9   |
| 678 5   678 | 9  3 18  | 2    4    167 |
| 4   9   2   | 6  7 158 | 158  18   3   |
+-------------+----------+---------------+
| 9   16  3   | 5  8 2   | 4    167  167 |
| 168 7   68  | 4  9 3   | 16   5    2   |
| 2   4   5   | 1  6 7   | 9    3    8   |
+-------------+----------+---------------+
| 3   68  9   | 78 1 4   | 678  2    5   |
| 178 2   4   | 3  5 6   | 178  9    17  |
| 5   168 678 | 78 2 9   | 3    1678 4   |
+-------------+----------+---------------+

Play this puzzle online at the Daily Sudoku site
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Sep 27, 2008 9:22 am    Post subject: Reply with quote

The grid can be further reduced (8 in box 7 confined to col 2, and resulting cleanup) to
Code:

+--------------------------+--------------------------+--------------------------+
| 678     3       1        | 2       4       58       | 567     678     9        |
| 678     5       678      | 9       3       18       | 2       4       167      |
| 4       9       2        | 6       7       158      | 15      18      3        |
+--------------------------+--------------------------+--------------------------+
| 9       16      3        | 5       8       2        | 4       167     167      |
| 168     7       68       | 4       9       3        | 16      5       2        |
| 2       4       5        | 1       6       7        | 9       3       8        |
+--------------------------+--------------------------+--------------------------+
| 3       68      9        | 78      1       4        | 67      2       5        |
| 17      2       4        | 3       5       6        | 8       9       17       |
| 5       168     67       | 78      2       9        | 3       167     4        |
+--------------------------+--------------------------+--------------------------+

There is now an xy-wing 67-68-78 in boxes 7 and 8
and another one 16-67-17 in boxes 6 and 9.
No x-wing as far as I can see, but some other colorful options.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Sep 27, 2008 11:28 am    Post subject: Reply with quote

Quote:
The grid can be further reduced (8 in box 7 confined to col 2, and resulting cleanup)

Didn't understand that - can't see any further reductions from Crunched's grid. (Crunched's doesn't sound right)

But there is an x-wing on <1> (C17) which gives a one-step solution.
And another with an ER on <6>.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sat Sep 27, 2008 11:44 am    Post subject: Reply with quote

nataraj wrote:
The grid can be further reduced (8 in box 7 confined to col 2, and resulting cleanup) to
Code:

+--------------------------+--------------------------+--------------------------+
| 678     3       1        | 2       4       58       | 567     678     9        |
| 678     5       678      | 9       3       18       | 2       4       167      |
| 4       9       2        | 6       7       158      | 15      18      3        |
+--------------------------+--------------------------+--------------------------+
| 9       16      3        | 5       8       2        | 4       167     167      |
| 168     7       68       | 4       9       3        | 16      5       2        |
| 2       4       5        | 1       6       7        | 9       3       8        |
+--------------------------+--------------------------+--------------------------+
| 3       68      9        | 78      1       4        | 67      2       5        |
| 17      2       4        | 3       5       6        | 8       9       17       |
| 5       168     67       | 78      2       9        | 3       167     4        |
+--------------------------+--------------------------+--------------------------+

There is now an xy-wing 67-68-78 in boxes 7 and 8
and another one 16-67-17 in boxes 6 and 9.
No x-wing as far as I can see, but some other colorful options.


In fact Nataraj, I believe that two xy-wings <678> exist in boxes 7 and 8; the one you noted with pivot <68> at r7c2 and another with pivot <67> at r9c3. Both finish the puzzle.

Also, a x-wing <1> opens up after the xy-wing <167> that you also noted, but I fail to see any immediately after basics.

Ted
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sat Sep 27, 2008 11:55 am    Post subject: Reply with quote

cgordon wrote:
Quote:
The grid can be further reduced (8 in box 7 confined to col 2, and resulting cleanup)

Didn't understand that - can't see any further reductions from Crunched's grid. (Crunched's doesn't sound right)

But there is an x-wing on <1> (C17) which gives a one-step solution.
And another with an ER on <6>.


Craig, all of the candidate digit <8> for col 2 reside in box 7, thus the two additional <8s> in box <7>, r8c1 & r9c3, can be eliminated as noted by Nataraj.

Also, when I look at the code posted by "crunched", I see a <1> in r3c7, which invalidates the x-wing you noted.

Ted
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Sep 27, 2008 12:01 pm    Post subject: Reply with quote

cgordon wrote:
Quote:
The grid can be further reduced (8 in box 7 confined to col 2, and resulting cleanup)

Didn't understand that - can't see any further reductions from Crunched's grid.


Craig,
8 in column 2 is confined to two cells: r7c2 and r9c2.

Therefore, in crunched's grid, 8 is not a candidate in r8c1 and r9c3. This is called a box-line interaction and usually is regarded as one of the basic techniques. This is why I said "...can be further reduced".

With 8 gone from r8c1, the naked pair 17 in r8c19 leaves 8 as a naked single in r8c7 and I definitely see no x-wing (1) in cols 1 and 7.

@tlanglet: Quite right, Ted! There are two overlapping xy-wings, one eliminating 7 and one eliminating 8 from the pair in r79c7. After the xy-wing I went on to solve the puzzle without more advanced moves (at least not that I remember). It is quite possible that there are any number of x-wings or even more exotic creatures, I just did not look for them.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Sep 27, 2008 12:13 pm    Post subject: Reply with quote

Ted/Nataraj: Yes - I see the <8> elimination now - I have difficulty spotting those things. And there is no x-wing - that was merely Friday night/Saturday morning brain damage. But eh !! There was an ER on <6>
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Sep 27, 2008 12:37 pm    Post subject: Reply with quote

cgordon wrote:
Ted/Nataraj: Yes - I see the <8> elimination now - I have difficulty spotting those things. And there is no x-wing - that was merely Friday night/Saturday morning brain damage. But eh !! There was an ER on <6>


the ER is there for sure:

Box 4 together with strong link (6) in row7 make r5c7=1.

Now that I look at the grid more closely, there is also a
w-wing(6) r7c7=r9c3 via strong link on 7 in col 4 and it removes 6 from r7c2 and r9c8
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Sep 27, 2008 3:56 pm    Post subject: Reply with quote

Let me redeem myself. With the removal of the <8>s in Box 7 we are left with an x wing on <8>. Doesn't do much - but that's not the point.
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Clement



Joined: 24 Apr 2006
Posts: 1110
Location: Dar es Salaam Tanzania

PostPosted: Sat Sep 27, 2008 6:04 pm    Post subject: Daily Sudoku: Sat 27-Sep-2008 VH Reply with quote

XY-Wing (678) Pivot in r7c2 with candidates {6,8} eliminating 7 in r9c4 solves the puzzle. Smile
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Clement



Joined: 24 Apr 2006
Posts: 1110
Location: Dar es Salaam Tanzania

PostPosted: Sat Sep 27, 2008 7:15 pm    Post subject: Reply with quote

XY-Wing (678) Pivot in r7c2 {6,8} eliminating 7 in r9c4 solves the puzzle.
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crunched



Joined: 05 Feb 2008
Posts: 168

PostPosted: Sat Sep 27, 2008 7:43 pm    Post subject: Reply with quote

If one never noticed the 8 reduction in Box 7 (that would include me) then an 8 wing in columns 2, 4 does much. It removes several 8s and helps open up the xy wing which wins the derby.

cgordon wrote:
Let me redeem myself. With the removal of the <8>s in Box 7 we are left with an x wing on <8>. Doesn't do much - but that's not the point.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Sep 27, 2008 8:48 pm    Post subject: Reply with quote

Shocked I am amazed to see that a basic move destroys a Wing which solves the puzzle. I got to here:
Code:
+----------------+----------------+----------------+
| 678  3    1    | 2    4    58   | 5678 678  9    |
| 678  5    678  | 9    3    18   | 2    4    167  |
| 4    9    2    | 6    7    158  | 158  18   3    |
+----------------+----------------+----------------+
| 9    16   3    | 5    8    2    | 4    167  167  |
| 168  7    68   | 4    9    3    | 16   5    2    |
| 2    4    5    | 1    6    7    | 9    3    8    |
+----------------+----------------+----------------+
| 3    68@  9    | 78   1    4    | 678  2    5    |
| 178  2    4    | 3    5    6    | 178  9    17   |
| 5   16-8  678@ | 78@  2    9    | 3    1678 4    |
+----------------+----------------+----------------+
There is an XYZ-wing <678> that takes out <8> in R9C2 and solves the puzzle in one step.

I did not notice the elimination of <8> in B7C13 as discussed above!

Keith

(I do see now that the XYZ-wing becomes an XY-wing, making the same elimination.)
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat Sep 27, 2008 9:25 pm    Post subject: Reply with quote

My one step was a W-Wing on 67. I don't see any grids here that offer the possibility, so I probably missed something that others caught.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Sep 27, 2008 10:12 pm    Post subject: Reply with quote

Marty, my grid "after basics" above does indeed offer the possibility
nataraj wrote:
Now that I look at the grid more closely, there is also a
w-wing(6) r7c7=r9c3 via strong link on 7 in col 4 and it removes 6 from r7c2 and r9c8
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sun Sep 28, 2008 12:05 am    Post subject: Reply with quote

nataraj wrote:
Marty, my grid "after basics" above does indeed offer the possibility
nataraj wrote:
Now that I look at the grid more closely, there is also a
w-wing(6) r7c7=r9c3 via strong link on 7 in col 4 and it removes 6 from r7c2 and r9c8

It does indeed, but I'm thinking mine was in boxes 13. At any rate, if that is correct, I couldn't replicate the situation when I tried it a second time, this time online.
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