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Salsa #6 -- Advanced (wings on steroids)

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 14, 2009 4:32 pm Post subject: Salsa #6 -- Advanced (wings on steroids)

I've moved finned/Sashimi X-Wing to VH+

Code:

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

Play this puzzle online at the Daily Sudoku site

===== ===== ===== ===== ===== ===== ===== ===== ===== Ratings are Accumulative

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

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

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

VH+: 2-String Kite, Empty Rectangle, Remote Pair, Skyscraper, Colors, UR Type 2, finned/Sashimi X-Wing

Advanced: Multiple Colors, Swordfish, M-Wing, W-Wing, XY-Chain

Extreme: Jellyfish, (but mostly) Chain

wapati

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

Posted: Sat Feb 14, 2009 5:19 pm Post subject:

I don't know what wings are present. I used a 4-cell xy-chain and a 5-cell xy-chain.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 14, 2009 6:28 pm Post subject:

wapati wrote:

I don't know what wings are present.
I used a 4-cell xy-chain and a 5-cell xy-chain.

Wings on Steroids: M/W-Wings that are atypical; i.e., extended internally beyond the typical 4-cell configuration.

wapati

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

Posted: Sat Feb 14, 2009 8:08 pm Post subject:

This is equivalent to the 5-cell xy-chain I used. What other name could one call it?

Code:

.------------------.------------------.------------------.
| 9 16 8 | 3 146 1467 | 2 5 17 |
| 3 5 12 | 127 9 8 | 4 6 17 |
| 4 126 7 | 12 5 16 | 3 9 8 |
:------------------+------------------+------------------:
| 16 14 46 | 8 3 9 | 7 2 5 |
| 7 8 25 | 56 246 456 | 1 3 9 |
|*25 3 9 | 17 #12 57-1 | 8 4 6 |
:------------------+------------------+------------------:
|*25 9 125 | 4 8 #13 | 6 7 #23 |
| 16 7 3 | 9 6-1 2 | 5 8 4 |
| 8 24 46 | 56 7 356 | 9 1 23 |
'------------------'------------------'------------------'

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 14, 2009 10:32 pm Post subject:

wapati wrote:

This is equivalent to the 5-cell xy-chain I used. What other name could one call it?

You have a perfectly acceptable 5-cell XY-Chain. In this forum, it could also be called an XY-Wing with pincher extension on both wing cells. That's not what I'm describing.

Here's the Eureka notation for a W-Wing and a generalized 4-cell M-wing.

Code:

gM-Wing: (Y=X)a - (X)b = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

W-Wing: (Y=X)a - (X)b = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

Here's the Eureka notation for a W-Wing and a generalized M-Wing on steroids. Multiple internal strong links in the X digit are used to extend the pattern.

Code:

gM-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

W-Wing: (Y=X)a - (X)b ... = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

Think of a (222) Swordfish that does not produce any eliminations, but opposing vertices can be extended to cells that can produce an elimination.

[Edit: several corrections.]

Last edited by daj95376 on Fri Feb 20, 2009 1:29 am; edited 2 times in total

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sat Feb 14, 2009 10:55 pm Post subject:

daj95376 wrote:

Here's the Eureka notation for a generalized 4-cell M/W-wing.

Code:

gM-Wing: (Y=X)a - (X)b = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

gW-Wing: (Y=X)a - (X)b = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

Here's the Eureka notation for a generalized M/W-Wing on steroids. Multiple internal strong links in the X digit are used to extend the pattern.

Code:

_M-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

_W-Wing: (Y=X)a - (X)b ... = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

That's not the way I learned it. Because of location of the ellipsis, the 1st code block looks like the normal m/w-wings and the 2nd has the generalized m/w-wings.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 14, 2009 11:27 pm Post subject:

ronk wrote:

That's not the way I learned it. Because of location of the ellipsis, the 1st code block looks like the normal m/w-wings and the 2nd has the generalized m/w-wings.

I was afraid there'd be confusion. Here it is with all of the I's crossed and all of the T's dotted.

Note: The original M-Wing and W-Wing definitions had additional strong link restrictions that are not present in the generalized notation!

First, the generalized form of M-Wing, and a W-Wing (as I understand them).

Code:

gM-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

W-Wing: (Y=X)a - (X)b = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

The ellipsis in gM-Wing means that the pattern can be extended beyond four cells. The lack of an ellipsis in the W-Wing means that it isn't (normally) defined beyond four cells.

In my first box of coding (that you quoted), I specifically stated that I was talking about 4-cell M/W-Wings. Thus, I removed the ellipsis from gM-Wing. This box represents how most W-Wings and (generalized) M-Wings are found.

In my second box, I replaced "g" with "_", and this was a big mistake. The notation for "_M-Wing" in this box is really the notation for gM-Wing (see above). The notation for "_W-Wing" is new ... and implies that more than four cells are possible -- using strong links on the X digit.

Now, keith and others are free to correct my correction!

[Edit: I made corrections to the W-Wing description.]

Last edited by daj95376 on Fri Feb 20, 2009 1:32 am; edited 2 times in total

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Feb 15, 2009 3:51 pm Post subject:

Maybe it's best that I provide a solution and put this puzzle (and topic) to rest.

Code:

+--------------------------------------------------------------+
| 9 24 5 | 248 1 3 | 478 27 6 |
| 14 3 8 | 6 27 279 | 14 29 5 |
| 146 7 1246 | 2489 24 5 | 148 129 3 |
|--------------------+--------------------+--------------------|
| 1478 6 1247 | 5 9 27 | 17 3 248 |
| 5 124 1247 | 3 8 6 | 9 17 24 |
| 78 9 3 | 24 247 1 | 5 6 28 |
|--------------------+--------------------+--------------------|
| 2 5 9 | 1 3 4 | 6 8 7 |
| 3 14 14 | 7 6 8 | 2 5 9 |
| 67 8 67 | 29 5 29 | 3 4 1 |
+--------------------------------------------------------------+
# 53 eliminations remain

W-Wing: (Y=X)a -(X)b =(X)c -(X=Y)d

W-Wing: (2=7)r1c8-(7)r5c8 =(7)r2c6-(7=2)r2c5 => [r1c4],[r2c8]<>2
steroid: =r4c7-r4c6
__________________________________________________________________________

Code:

+--------------------------------------------------------------+
| 9 24 5 | 8 1 3 | 47 27 6 |
| 14 3 8 | 6 27 27 | 14 9 5 |
| 16 7 126 | 9 4 5 | 8 12 3 |
|--------------------+--------------------+--------------------|
| 1478 6 1247 | 5 9 27 | 17 3 248 |
| 5 124 1247 | 3 8 6 | 9 17 24 |
| 78 9 3 | 4 27 1 | 5 6 28 |
|--------------------+--------------------+--------------------|
| 2 5 9 | 1 3 4 | 6 8 7 |
| 3 14 14 | 7 6 8 | 2 5 9 |
| 67 8 67 | 2 5 9 | 3 4 1 |
+--------------------------------------------------------------+
# 35 eliminations remain

gM-Wing: (Y=X)a -(X)b ... =(X-Y)r =(Y)s

=(4)r1c2 => [r8 c2]<>4
gM-Wing: (4=1)r8c3-(1)r8c2 =(1-4)r2c1=(4)r4c1 => [r45c3]<>4
steroid: =r5c2-r5c8=r3c8-r2c7
______________________________________________________________________________

Code:

r5 Naked Pair <> 24 [r5c3]
r4 Naked Triple <> 127 [r4c19]
c3b4 Locked Candidate 1 <> 1 [r3c3]

BUG+1 = 7 [r4c3]

[Edit: still correcting W-Wing description.]

Last edited by daj95376 on Fri Feb 20, 2009 1:34 am; edited 1 time in total

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sun Feb 15, 2009 6:48 pm Post subject:

daj95376 wrote:

First, the generalized form of M-Wing and W-Wing (as I understand them).

Code:

gM-Wing: (Y=X)a - (X)b ... = (X-Y)r = (Y)s => eliminations in peers of [a] and [s] for (Y)

gW-Wing: (Y=X)a - (X)b = (X)c - (X=Y)d => eliminations in peers of [a] and [d] for (Y)
_____________________________________________________________________________________________

The ellipsis in gM-Wing means that the pattern can be extended beyond four cells. The lack of an ellipsis in the gW-Wing means that it isn't (normally) defined beyond four cells.

Not exactly a poster child for consistency, is it?

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Feb 15, 2009 7:31 pm Post subject:

ronk wrote:

Not exactly a poster child for consistency, is it?

Sudoku ... consistent? Laughing

Seriously. From what I can tell, the original M-Wing and W-Wing definitions were perfect for hand solvers to find a couple of additional patterns. All of the weak inferences required a strong link (I believe).

Over time, the generalized versions appeared -- except the ellipsis was never added to the W-Wing. I kept meaning to ask Keith if it could be added, but my swiss-cheese memory never kicked in at the right time.

Of course, all of the above is contingent on my having the current definitions correct in the first place. Something you know from experience isn't worth ??????? a wooden nickel on. Very Happy

For some reason, the processor wants to turn my word b-e-t-t-i-n-g into a string of question marks. It's correct in the composition window!

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Feb 15, 2009 10:29 pm Post subject:

Quote:

For some reason, the processor wants to turn my word b-e-t-t-i-n-g into a string of question marks. It's correct in the composition window!

perhaps this is an anti-gambling site?
-----

Code:

.------------------.------------------.------------------.
| 9 24 5 | 248 1 3 | 478 27 6 |
| 14 3 8 | 6 27 279 | 14 29 5 |
| 146 7 1246 | 2489 24 5 | 148 129 3 |
:------------------+------------------+------------------:
|147[8] 6 1247 | 5 9 2[7] |1[7] 3 2-4[8] |
| 5 U124 U1247 | 3 8 6 | 9 [17] 2[4] |
|[78] 9 3 | 24 24[7] 1 | 5 6 28 |
:------------------+------------------+------------------:
| 2 5 9 | 1 3 4 | 6 8 7 |
| 3 U14 U14 | 7 6 8 | 2 5 9 |
| 67 8 67 | 29 5 29 | 3 4 1 |
'------------------'------------------'------------------'

the UR{1,4} in r58c23 tells us that neither the 1 in r5c8 nor the 4 in r5c9 can both be false or the deadly pattern is forced to exist.
so this inference can be made between them
UR[(4)r5c9 = (1)r5c8]
this can then be extended to eliminate the 4 in r4c9...

UR[(4)r5c9 = (1)r5c8] - (7)r5c8 = (7)r4c7 - (7)r4c6 = (7)r6c5 - (7=8)r6c1 - (8)r4c1 = (8)r4c9; r4c9 <> 4

leaves this xy-wing to finish.

Code:

.------------------.------------------.------------------.
| 9 -24 5 | 248 1 3 | 478 #27 6 |
| 14 3 8 | 6 27 279 | 14 29 5 |
| 146 7 1246 | 2489 24 5 | 148 129 3 |
:------------------+------------------+------------------:
| 1478 6 1247 | 5 9 27 | 17 3 28 |
| 5 #12 127 | 3 8 6 | 9 #17 4 |
| 78 9 3 | 24 247 1 | 5 6 28 |
:------------------+------------------+------------------:
| 2 5 9 | 1 3 4 | 6 8 7 |
| 3 14 14 | 7 6 8 | 2 5 9 |
| 67 8 67 | 29 5 29 | 3 4 1 |
'------------------'------------------'------------------'

xy-wing {1,2,7} removes 2 from r1c2

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