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Set H Puzzle 45

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Jan 07, 2009 8:51 pm    Post subject: Set H Puzzle 45 Reply with quote

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

Play this puzzle online at the Daily Sudoku site

===== ===== ===== ===== ===== ===== ===== ===== ===== ===== ===== ===== =====

Can be solved using steps from ...

Basics: Naked/Hidden Single, Naked Pair/Triple, Locked Candidate 1/2

Basics+: Naked Quad, Hidden Pair/Triple/Quad

VH: BUG+1, Remote Pair, UR Type 1, X-Wing, XY-Wing

Advanced: 2-String Kite, Empty Rectangle, Skyscraper, UR Type 2, XYZ-Wing

Extreme: finned X-Wing, M-Wing, W-Wing, XY-Chain

Extreme+: Swordfish, Jellyfish, (but mostly) Chain
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Thu Jan 08, 2009 1:18 am    Post subject: Reply with quote

I must've missed something, as it took me 11 steps, ending with a BUG+1.

I did have an interesting little pattern that I don't recall seeing before. Something like below:

Code:

+---------+-------+---------+
| .  .  . | . . . | . .  .  |
| .  .  . | . . . | . .  .  |
| .  .  . | . . . | . .  .  |
+---------+-------+---------+
| .  .  . | . . . | . .  .  |
| .  .  . | . . . | . .  .  |
| .  .  . | . . . | . .  .  |
+---------+-------+---------+
| .  25 . | . . . | . .  28 |
| .  .  . | . . . | . .  .  |
| 24 .  . | . . . | . 12 .  |
+---------+-------+---------+

Play this puzzle online at the Daily Sudoku site

The 2s are strong links in both rows 7 and 9. There were 2s in row 8 in both boxes. So two separate skyscrapers, or multi-colorings, on the same numbers, made eliminations in both boxes.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Jan 08, 2009 1:42 am    Post subject: Reply with quote

Marty R. wrote:
I must've missed something, as it took me 11 steps, ending with a BUG+1.

I was afraid this puzzle might cause problems.

Hint wrote:
Skyscraper [r17].

Later wrote:
Remote Pair in a Skyscraper pattern causes several eliminations.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Thu Jan 08, 2009 2:40 pm    Post subject: Reply with quote

daj95376 wrote:

I was afraid this puzzle might cause problems.

Danny, I think this was a great puzzle. It was long for me also, taking seven steps, but it was fun. I much prefer a long VH puzzle over a one-stepper VH.

I also had a situation of two VH techniques interacting; a remote pair with a Type 1 UR. Either one alone destroyed the other, but viewed together it set r4c8=1.

Ted Smile
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Jan 08, 2009 4:24 pm    Post subject: Reply with quote

tlanglet wrote:
Danny, I think this was a great puzzle. It was long for me also, taking seven steps, but it was fun. I much prefer a long VH puzzle over a one-stepper VH.

I also had a situation of two VH techniques interacting; a remote pair with a Type 1 UR. Either one alone destroyed the other, but viewed together it set r4c8=1.

Hello Ted, I'm glad that you enjoyed this puzzle, but I suspect that others don't agree that it was fun. The wrinkle in the Set H puzzles is that one or more Advanced step is needed in the solution. This creates a different situation than running across a Kite/ER/Skyscraper (for example) when they're present but not needed.

I found the UR_1 to be extraneous. The Remote Pair was sufficient. What amazes me is that there wasn't any mention of the two XY-Wings needed at the end. They both needed the eliminations in [r5c6] from the Remote Pair in order to exist.

I'm going to continue to post puzzles from Set H because I think the challenges they present will be worthwhile, even to those who don't solve them completely. However, I'm also going to look for some less demanding Set N puzzles to post at the same time.

Regards, Danny
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Thu Jan 08, 2009 4:37 pm    Post subject: Reply with quote

Quote:
I found the UR_1 to be extraneous. The Remote Pair was sufficient. What amazes me is that there wasn't any mention of the two XY-Wings needed at the end. They both needed the eliminations in [r5c6] from the Remote Pair in order to exist.

I don't remember specifics, all I have is my notes on what steps I used. I had seven assorted steps before the Remote Pairs (which could also be viewed as skyscrapers), following which were the two XY-Wings leading to the BUG+1.
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wapati



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

PostPosted: Thu Jan 08, 2009 5:00 pm    Post subject: Reply with quote

daj95376 wrote:

I found the UR_1 to be extraneous. The Remote Pair was sufficient. What amazes me is that there wasn't any mention of the two XY-Wings needed at the end. They both needed the eliminations in [r5c6] from the Remote Pair in order to exist.


I found that only one xy-wing is needed getting you to here where a UR, a BUG, or an XY finishes. Everyone seems to tread different trails!

Code:
.---------------.---------------.---------------.
| 6    2    1   | 38   47   47  | 38   9    5   |
| 7    3    8   | 1    9    5   | 2    6    4   |
| 9    4    5   | 2    36   68  | 7    38   1   |
:---------------+---------------+---------------:
| 48   6    9   | 38   34   2   | 5    1    7   |
| 14   7    23  | 5    146  46  | 38   238  9   |
| 18   5    23  | 9    17   78  | 4    23   6   |
:---------------+---------------+---------------:
| 3    8    6   | 7    5    9   | 1    4    2   |
| 5    1    4   | 6    2    3   | 9    7    8   |
| 2    9    7   | 4    8    1   | 6    5    3   |
'---------------'---------------'---------------'
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Thu Jan 08, 2009 6:27 pm    Post subject: Reply with quote

Quote:
I found that only one xy-wing is needed getting you to here where a UR, a BUG, or an XY finishes. Everyone seems to tread different trails!

OK, I'm trying this a second time, this time online, where I'm less confident than with pencil and paper. I must be missing something in the basics, because I don't see an XY-Wing and am stuck on basics.

Code:

+----------------+------------------+------------------+
| 6     248 1    | 348   347   3478 | 238  9      5    |
| 7     3   28   | 1     9     5    | 268  268    4    |
| 9     48  5    | 2     346   3468 | 7    38     1    |
+----------------+------------------+------------------+
| 1348  6   9    | 348   1347  2    | 5    1378   78   |
| 12348 7   2348 | 34568 13456 3468 | 2368 12368  9    |
| 1238  5   238  | 9     1367  3678 | 4    123678 2678 |
+----------------+------------------+------------------+
| 35    28  6    | 7     35    9    | 1    4      28   |
| 3458  1   348  | 3456  2     346  | 9    5678   678  |
| 245   9   7    | 456   8     1    | 26   256    3    |
+----------------+------------------+------------------+

Play this puzzle online at the Daily Sudoku site
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cgordon



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

PostPosted: Thu Jan 08, 2009 7:41 pm    Post subject: Reply with quote

I really enjoyed this one - a whole plethora of good stuff. Colouring gets rid of <2> in R6C1, R9C7; a UR on 78; an ER on <3> and skyscrapers on <3> and <8> .

Not sure about your classifications - is that a statistical thing or a subjective thing? For me ER's and Skyscrapers are easier than Remote Pairs and xy-wings. What about Type 4 UR's or Type 3 UR's (I have yet to find one of them). Swordfish and Jellyfish should be banned. Just musing!
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Jan 08, 2009 8:19 pm    Post subject: Reply with quote

Marty,
AFAIK, you are correct on your grid, and you are also right about no xy-wings being present, in fact there aren't any xy, xyz or x-wings present and no UR's. and no direct w-wings.

Code:
.------------------------.------------------------.------------------------.
| 6      W248     1      | 348     347     3478   |E238     9       5      |
| 7       3      W28     | 1       9       5      |E268    E268     4      |
| 9      W48      5      | 2       346     3468   | 7       38      1      |
:------------------------+------------------------+------------------------:
| 1348    6       9      | 348     1347    2      | 5       1378    78     |
| 12348   7       2348   | 34568   13456   3468   | 2368    12368   9      |
| 1238    5       238    | 9       1367    3678   | 4       123678  2678   |
:------------------------+------------------------+------------------------:
| 35     W28      6      | 7       35      9      | 1       4      W28     |
| 3458    1       348    | 3456    2       346    | 9       5678    678    |
| 245     9       7      | 456     8       1      |-26      256     3      |
'------------------------'------------------------'------------------------'

this is a grouped extended w-wing... the W-wing is marked with "w" notice the grouped link in box 1... the extension is marked with "E" notice the grouped extension in box 3. eliminates 2 in r9c7

(2=8)r7c9 - (8)r7c2 = (8)r13c2 - (8=2)r2c3 - (2)r2c78 = (2)r1c7; r9c7 <> 2

Code:
.---------------------.---------------------.---------------------.
| 6      2      1     |*38     47     47    |*38     9      5     |
| 7      3      8     | 1      9      5     | 2      6      4     |
| 9      4      5     | 2      36     368   | 7      38     1     |
:---------------------+---------------------+---------------------:
| 1348   6      9     |*38     1347   2     | 5      1378   78    |
| 1348   7      234   | 56     13456  3468  |*38     1238   9     |
| 138    5      23    | 9      137    378   | 4      12378  6     |
:---------------------+---------------------+---------------------:
| 35     8      6     | 7      35     9     | 1      4      2     |
| 345    1      34    | 56     2      36    | 9      78     78    |
| 2      9      7     | 4      8      1     | 6      5      3     |
'---------------------'---------------------'---------------------'

the marked remote pair eliminates any other 3's and 8's that both r4c4 and r5c7 see....
r5c56 <> 3, r4c8 <> 3
r5c6 <> 8, r4c89 <> 8
-----
then two more xy-wings finish it.
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wapati



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

PostPosted: Thu Jan 08, 2009 9:23 pm    Post subject: Reply with quote

Marty R. wrote:

OK, I'm trying this a second time, this time online, where I'm less confident than with pencil and paper. I must be missing something in the basics, because I don't see an XY-Wing and am stuck on basics.


I did mean that only one of the two xy-wings daj mentioned is needed, and it comes after a skyscraper and then the 38 remote pair or 38 double-sky.

From your position I would use this skyscraper, and after that basic stuff, to proceed to the remote-pair that daj mentioned which exposes two xy-wings, one of which is very useful.
Code:
+----------------+------------------+------------------+
| 6    #248 1    | 348   347   3478 |#238  9      5    |
| 7     3   28   | 1     9     5    | 268  268    4    |
| 9     48  5    | 2     346   3468 | 7    38     1    |
+----------------+------------------+------------------+
| 1348  6   9    | 348   1347  2    | 5    1378   78   |
| 12348 7   2348 | 34568 13456 3468 | 2368 12368  9    |
| 1238  5   238  | 9     1367  3678 | 4    123678 2678 |
+----------------+------------------+------------------+
| 35   *28  6    | 7     35    9    | 1    4     *28   |
| 3458  1   348  | 3456  2     346  | 9    5678   678  |
| 245   9   7    | 456   8     1    | 6-2  256    3    |
+----------------+------------------+------------------+


38 double sky.
Code:
.---------------------.---------------------.---------------------.
| 6      2      1     |*38     47     47    |#38     9      5     |
| 7      3      8     | 1      9      5     | 2      6      4     |
| 9      4      5     | 2      36     368   | 7      38     1     |
:---------------------+---------------------+---------------------:
| 1348   6      9     |*38     1347   2     | 5      17-38  7-8   |
| 1348   7      234   | 56     1456-3  46-38|#38     1238   9     |
| 138    5      23    | 9      137    378   | 4      12378  6     |
:---------------------+---------------------+---------------------:
| 35     8      6     | 7      35     9     | 1      4      2     |
| 345    1      34    | 56     2      36    | 9      78     78    |
| 2      9      7     | 4      8      1     | 6      5      3     |
'---------------------'---------------------'---------------------'


Sorry for the confusion. Embarassed
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jan 09, 2009 2:10 am    Post subject: Reply with quote

Here's my solution, with annotated notes, from the beginning. All that's missing is Singles.

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

 r7      Naked  Pair                     <> 28   [r7c15]
 r3  b2  Locked Candidate 1              <> 6    [r3c8]

Code:
 +--------------------------------------------------------------------------------+
 |  6       248     1       |  348     347     3478    |  238     9       5       |
 |  7       3       28      |  1       9       5       |  268     268     4       |
 |  9       48      5       |  2       346     3468    |  7       38      1       |
 |--------------------------+--------------------------+--------------------------|
 |  1348    6       9       |  348     1347    2       |  5       1378    78      |
 |  12348   7       2348    |  34568   13456   3468    |  2368    12368   9       |
 |  1238    5       238     |  9       1367    3678    |  4       123678  2678    |
 |--------------------------+--------------------------+--------------------------|
 |  35      28      6       |  7       35      9       |  1       4       28      |
 |  3458    1       348     |  3456    2       346     |  9       5678    678     |
 |  245     9       7       |  456     8       1       |  26      256     3       |
 +--------------------------------------------------------------------------------+
 # 105 eliminations remain

         2x Empty Rectangle              <> 2    [r6c1],[r9c7]    only one needed
 r17     Skyscraper                      <> 2           [r9c7]    alternate

   c4    Naked  Pair                     <> 38   [r58c4]
 r1      Naked  Pair                     <> 38   [r1c56]

Code:
 +-----------------------------------------------------------------------+
 |  6      2      1      |  38     47     47     |  38     9      5      |
 |  7      3      8      |  1      9      5      |  2      6      4      |
 |  9      4      5      |  2      36     368    |  7      38     1      |
 |-----------------------+-----------------------+-----------------------|
 |  1348   6      9      |  38     1347   2      |  5      1378   78     |
 |  1348   7      234    |  56     13456  3468   |  38     1238   9      |
 |  138    5      23     |  9      137    378    |  4      12378  6      |
 |-----------------------+-----------------------+-----------------------|
 |  35     8      6      |  7      35     9      |  1      4      2      |
 |  345    1      34     |  56     2      36     |  9      78     78     |
 |  2      9      7      |  4      8      1      |  6      5      3      |
 +-----------------------------------------------------------------------+
 # 56 eliminations remain

         UR Type 1 [r48c89]              <> 78   [r4c8]           extraneous

         Remote Pair                     <> 3    [r4c8],[r5c56]   Skyscraper pattern
           "     "                       <> 8    [r4c89],[r5c6]       "         "

Code:
 +--------------------------------------------------------------+
 |  6     2     1     |  38    47    47    |  38    9     5     |
 |  7     3     8     |  1     9     5     |  2     6     4     |
 |  9     4     5     |  2     36    368   |  7     38    1     |
 |--------------------+--------------------+--------------------|
 |  348   6     9     |  38    34    2     |  5     1     7     |
 |  1348  7     234   |  56    1456  46    |  38    238   9     |
 |  138   5     23    |  9     137   378   |  4     238   6     |
 |--------------------+--------------------+--------------------|
 |  35    8     6     |  7     35    9     |  1     4     2     |
 |  345   1     34    |  56    2     36    |  9     7     8     |
 |  2     9     7     |  4     8     1     |  6     5     3     |
 +--------------------------------------------------------------+
 # 41 eliminations remain

         XY-Wing  [r4c5]/[r3c5]+[r5c6]   <> 6    [r3c6],[r5c5]
         XY-Wing  [r5c6]/[r4c5]+[r8c6]   <> 3    [r6c6],[r7c5]
         XY-Wing  [r8c6]/[r5c6]+[r8c3]   <> 4    [r5c3]           extraneous

Of the three XY-Wings present at the end, it appears that wapati chose the XY-Wing with pivot [r5c6]. If he'd also performed the XY-Wing with pivot [r4c5], then Singles would have completed the puzzle.

When I said there were two XY-Wings needed at the end, I wasn't clear that it was to reduce the puzzle to Singles.
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