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Salsa #1

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Jan 11, 2009 1:09 pm    Post subject: Salsa #1 Reply with quote

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
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Mon Jan 12, 2009 3:27 am    Post subject: Reply with quote

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
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jan 13, 2009 11:14 am    Post subject: Reply with quote

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?
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Jan 13, 2009 7:15 pm    Post subject: Reply with quote

ronk wrote:
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?

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!
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Jan 13, 2009 7:54 pm    Post subject: Reply with quote

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.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Jan 14, 2009 3:03 pm    Post subject: Reply with quote

daj95376 wrote:

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.

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.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Wed Jan 14, 2009 7:36 pm    Post subject: Reply with quote

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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