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Set H Puzzle 45

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Wed Jan 07, 2009 8:51 pm Post subject: Set H Puzzle 45

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

Marty R.

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

Posted: Thu Jan 08, 2009 1:18 am Post subject:

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.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Jan 08, 2009 1:42 am Post subject:

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.

tlanglet

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

Posted: Thu Jan 08, 2009 2:40 pm Post subject:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Jan 08, 2009 4:24 pm Post subject:

tlanglet wrote:

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

Marty R.

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

Posted: Thu Jan 08, 2009 4:37 pm Post subject:

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.

wapati

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

Posted: Thu Jan 08, 2009 5:00 pm Post subject:

daj95376 wrote:

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 |
'---------------'---------------'---------------'

Marty R.

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

Posted: Thu Jan 08, 2009 6:27 pm Post subject:

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

cgordon

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

Posted: Thu Jan 08, 2009 7:41 pm Post subject:

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!

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Thu Jan 08, 2009 8:19 pm Post subject:

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.

wapati

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

Posted: Thu Jan 08, 2009 9:23 pm Post subject:

Marty R. wrote:

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

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Jan 09, 2009 2:10 am Post subject:

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

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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