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Salsa #1

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Jan 11, 2009 1:09 pm Post subject: Salsa #1

Code:

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

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

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Mon Jan 12, 2009 3:27 am Post subject:

Code:

.---------------------.---------------------.---------------------.
| 2 4 5 | 1678 368 1678 | 1369 139 1369 |
|*13 9 8 | 5 2 -16 | 136 4 7 |
| 6 7 *13 |*19 39 4 | 5 8 2 |
:---------------------+---------------------+---------------------:
|*37 5 39 | 689 1 689 |*3679 2 4 |
| 137 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:---------------------+---------------------+---------------------:
| 589 3 4 |-16789 5689 16789 | 2 179 189 |
| 589 1 7 | 3 589 2 | 4 6 89 |
| 89 2 6 | 4 89 *17 |*137 137 5 |
'---------------------'---------------------'---------------------'

(1=7)r9c6 - (7)r9c7 = (7)r4c7 - (7=3)r4c1 - (3)r2c1 = (3-1)r3c3 = (1)r3c4; r7c4 and r2c6 is not 1

Code:

.------------------.------------------.------------------.
| 2 4 5 | 178 38 78 | 1369 139 1369 |
| 13 9 8 | 5 2 6 | 13 4 7 |
| 6 7 Y13 |Y19 39 4 | 5 8 2 |
:------------------+------------------+------------------:
| 37 5 Y39 |68-9 1 89 | 3679 2 4 |
| 137 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:------------------+------------------+------------------:
| 5 3 4 | 789 6 1789 | 2 179 189 |
| 89 1 7 | 3 5 2 | 4 6 89 |
| 89 2 6 | 4 89 17 | 137 137 5 |
'------------------'------------------'------------------'

xy-wing eliminates 9 from r4c4

Code:

.------------------.------------------.------------------.
| 2 4 5 | 178 *38 7-8 | 1369 139 1369 |
| 13 9 8 | 5 2 6 | 13 4 7 |
| 6 7 *13 | 19 *39 4 | 5 8 2 |
:------------------+------------------+------------------:
| 37 5 *39 | 68 1 *89 | 3679 2 4 |
| 137 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:------------------+------------------+------------------:
| 5 3 4 | 789 6 1789 | 2 179 189 |
| 89 1 7 | 3 5 2 | 4 6 89 |
| 89 2 6 | 4 89 17 | 137 137 5 |
'------------------'------------------'------------------'

(8=3)r1c5 - (3)r3c5 = (3)r3c4 - (3=9)r4c3 - (9=8)r4c6; r1c6 <> 8
this is also a xy-chain add the (9,1) cell... 83-39-91-13-39-98

Code:

.------------------.------------------.------------------.
| 2 4 5 | 18 38 7 | 1369 139 1369 |
|W13 9 8 | 5 2 6 |W13 4 7 |
| 6 7 13 | 19 39 4 | 5 8 2 |
:------------------+------------------+------------------:
|W37 5 39 | 68 1 89 |36-79 2 4 |
| 137 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:------------------+------------------+------------------:
| 5 3 4 | 7 6 89 | 2 19 189 |
| 89 1 7 | 3 5 2 | 4 6 89 |
| 89 2 6 | 4 89 1 |W37 37 5 |
'------------------'------------------'------------------'

W-wing {3,7}
(7=3)r4c1 - (3)r2c1 = (3)r2c7 - (3=7)r9c7; r4c7 <> 7

Code:

.------------------.------------------.------------------.
| 2 4 5 | 18 38 7 | 1369 139 *1369 |
|*13 9 8 | 5 2 6 |*13 4 7 |
| 6 7 13 | 19 39 4 | 5 8 2 |
:------------------+------------------+------------------:
| 7 5 39 | 68 1 89 | 369 2 4 |
|1-3 6 139 | 2 4 5 | 8 7 *39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:------------------+------------------+------------------:
| 5 3 4 | 7 6 89 | 2 19 189 |
| 89 1 7 | 3 5 2 | 4 6 89 |
| 89 2 6 | 4 89 1 | 7 3 5 |
'------------------'------------------'------------------'

the marked multicoloring on 3 finishes it.
{3}... r2c1 = r2c7 - r1c9 = r5c9; r5c1 <> 3

edit:
Mulligan taken on my initial Misleading M-wing; my mindblock made me make mind numbing misplacements.

Last edited by storm_norm on Tue Jan 13, 2009 7:30 pm; edited 2 times in total

ronk

Joined: 07 May 2006
Posts: 398

Posted: Tue Jan 13, 2009 11:14 am Post subject:

storm_norm wrote:

Code:

.---------------------.---------------------.---------------------.
| 2 4 5 |M1678 368 M1678 | 1369 139 1369 |
| 13 9 8 | 5 2 -16 | 136 4 7 |
| 6 7 13 |M19 39 4 | 5 8 2 |
:---------------------+---------------------+---------------------:
| 37 5 39 | 689 1 689 | 3679 2 4 |
| 137 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
:---------------------+---------------------+---------------------:
| 589 3 4 |-16789 5689 16789 | 2 179 189 |
| 589 1 7 | 3 589 2 | 4 6 89 |
| 89 2 6 | 4 89 M17 | 137 137 5 |
'---------------------'---------------------'---------------------'

the marked M-wing gets rid of the 1 in r7c4 and r2c6.

Just cruising around, trying to find out how people are using the m-wing term. How exactly does your deduction above work?

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Tue Jan 13, 2009 7:15 pm Post subject:

ronk wrote:

storm_norm wrote:

Code:

the marked M-wing gets rid of the 1 in r7c4 and r2c6.

Just cruising around, trying to find out how people are using the m-wing term. How exactly does your deduction above work?

I am not sure which hole this is, but I am taking a mulligan Cool

i'll gladly take my 6th shot on the par 4 if I can put it home from 9 feet.
honestly, I am not sure what I saw now that I look again. but, I have changed the chain in my first step to
(1=7)r9c6 - (7)r9c7 = (7)r4c7 - (7=3)r4c1 - (3)r2c1 = (3-1)r3c3 = (1)r3c4; r7c4 and r2c6 is not 1

very nice puzzle Danny!

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Tue Jan 13, 2009 7:54 pm Post subject:

Code:

after basics, Empty Rectangle on <3>, 2x XY-Wing
*--------------------------------------------------------------------*
| 2 4 5 | 178 368 1678 | 1369 139 1369 |
| 13 9 8 | 5 2 16 | 136 4 7 |
| 6 7 13 | 19 39 4 | 5 8 2 |
|----------------------+----------------------+----------------------|
| 37 5 39 | 68 1 89 | 3679 2 4 |
| 17 6 139 | 2 4 5 | 8 379 39 |
| 4 8 2 | 69 7 3 | 169 5 169 |
|----------------------+----------------------+----------------------|
| 589 3 4 | 1789 5689 16789 | 2 179 189 |
| 589 1 7 | 3 589 2 | 4 6 89 |
| 89 2 6 | 4 89 17 | 137 137 5 |
*--------------------------------------------------------------------*

Welcome RonK!!! (Sorry for using my solver's chain notation. I know you can handle it.)

Quantity in braces is overall effectiveness of (generalized) M/W-Wing.

Code:

{ 13} -1r9c6 7r9c6 7r4c7 7r5c1 1r2c1 [gM-Wing] <> 1 [r2c6]
{ 5} -9r5c3 9r4c3 9r7c6 9r8c9 [gM-Wing] <> 9 [r5c9]
{ 5} -3r5c9 9r5c9 9r6c4 9r3c5 3r1c5 [gM-Wing] <> 3 [r1c9]
{ 2} -3r4c3 9r4c3 9r6c4 9r3c5 3r3c3 [gM-Wing] <> 3 [r5c3]
{ 1} -8r9c5 9r9c5 9r4c6 8r4c4 [gM-Wing] <> 8 [r7c4]

{ 2} -3r4c3 9r4c3 9r7c6 9r8c9 3r5c9 [gW-Wing] <> 3 [r4c7],[r5c3]

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)
_____________________________________________________________________________________________

Note: The original definitions for M-Wing and W-Wing in this forum had additional strong links and bivalue cell restrictions that aren't present in the generalized versions.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Wed Jan 14, 2009 3:03 pm Post subject:

daj95376 wrote:

Code:

Note: The original definitions for M-Wing and W-Wing in this forum had additional strong links and bivalue cell restrictions that aren't present in the generalized versions.

Thanks for the example. So an m-wing is an x-cycle chain, with a xy bivalue tacked on one end, and a y-value bilocal on the other. That should be easy enough to remember.

However, I don't expect to be frequently using the term wing, even generalized, to a chain with more than three strong inferences.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Wed Jan 14, 2009 7:36 pm Post subject:

Quote:

However, I don't expect to be frequently using the term wing, even generalized, to a chain with more than three strong inferences

sounds like a good argument against why xy-wings are still called xy-wings, when the dirty little secret is they are xy-chains.

I guess names just stick, imagine that Smile

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