## Hybrid - Wings {work in progress}

Advanced methods and approaches for solving Sudoku puzzles

### Hybrid - Wings {work in progress}

This technique is not my own, some of it was documented by udosuk, danny, ronk, and my self
however
udosuk

"characteristically corrected by springs_999 late august 2018"

holds the original naming and was the first to publish documentation of these in a very long lost post on the old players forum and at that time something simplified was dubbed as " purple cows" as featured in xsudoku so the naming class type shall remain as i based these off the examples that program produced. {instead of the example springs suggested by said name}

A collection of 1-2+ bivalves with 3 strong links and 2 weak link interfaces among 4 cells:

there is multiple formations, so i will not be trying to document all minimal exemplars for these at this time i doubt its feasible to do so.

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`H1-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>XH2-Wing:  (X=Y)a - (Y)b = (Y-Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>XH3-Wing:  (X=Y)a - (Y=Z)b - (Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>XH4-Wing:  (X)a = (X)b - (X=Y)c - (Y=ZX)dx     no known restrictions on "a" and "dx" cell locations `

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` H1- wing .  /  . | .  /  . | .  .    . . A-C . | . C-A . | .  .    ..  /  . | .  /  . | .  .    .------------------------------.  /  . | .  /  . | .  .    . / AB+ / | / BC+ / | /  /    / .  /  . | .  /  . | .  .    .------------------------------.  /  . | .  /  . | .  .    . .  /  . | .  /  . | .  .    . .  /  . | .  /  . | .  .    .`

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`H1a- wing A  .  / | .  .  . | .  .    . A  . C-A| .  .  . | .  .    .A  .  / | .  .  . | .  .    .------------------------------/  .  / | .  .  . | .  .    . AB+/ BC+| /  /  / | /  /    / /  .  / | .  .  . | .  .    .------------------------------/  .  / | .  .  . | .  .    . /  .  / | .  .  . | .  .    . /  .  / | .  .  . | .  .    .`

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` H3 - wing.  .  . | .  .  . | .  /    . .  AB . | .  .  . | .  C-A    . .  .  . | .  .  . | .  /    .------------------------------.  .  . | .  .  . | .  /    . .  BC . | .  .  . | .  C    . .  .  . | .  .  . | .  /    .------------------------------.  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    .`

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` H3a - wing.  .  . | .  .  . | /  /    / .  AB . | .  .  . | /  C-A  / .  BC . | .  .  . | C  C    C ------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    ..  .  . | .  .  . | .  .    .------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .`

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` H2 - wing.  AB . | .  .  . | .  C-A  . .  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . ------------------------------.  .  . | .  .  . | .   /   . /  B  / | /  /  / | /  BC+  / .  .  . | .  .  . | .  /    . ------------------------------.  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . `

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` H2a - wing .  AB . | .  .  . | .  C-A   . .  .  . | .  .  . | .   /    . B  B  B | /  /  / | /   BC+  / ------------------------------.  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . ------------------------------.  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . .  .  . | .  .  . | .  /    . `

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` H4 - wing  {bi vavles are 49,34: this functions as the 48 cell and 348 are reduced to a pair consisting of 48,  or 4 is solved}     {to read this the strong link is only on digit 4 and 3} .  .  . | .  .  . | .  .    -4 /  49  / | /  /  / | /  /    48.  .  . | .  .  . | .  .    -4------------------------------.  .  . | .  .  . | .  .    -4 /  34  / | /  /  / | /  /  348    .  .  . | .  .  . | .  .    -4------------------------------.  .  . | .  .  . | .  .    -4 .  .  . | .  .  . | .  .    -4 .  .  . | .  .  . | .  .    -4`

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`  H4a w.t.f. - wing     {to read this the strong link is only on digit 4 and 3} .  .  . | .  .  . | -4  -4    -4 /  49  / | /  /  / | 4678~  4678~   4678~ /  34  / | /  /  / | /-4  34678*  /-4------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .`

this one is wonky, for every grouped node we can add +1 candidate to the * cell that is found in the ~ cells
when 49 is 4 we have a naked triple left in the grouped node ~ cells, and the 34 bivalve removes 3 from the * cell leaving it solved as 4.
when 49 is 9 we know the grouped link contains 4.
thus all peer cells of the ~ and * cells cannot contain 4

Code: Select all
`  H4b w.t.f. - wing       {to read this the strong link is only on digit 4 and 3} .  .  . | .  .  . | -4  -4    -4 /  49  / | /  /  / | 456789~  456789~   456789~ /  34  / | /  /  / | 3456789*  3456789*  3456789*------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .`

same as type 4a, by expanding the * cells we have an almost almost subset size 6.

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`h5a - wing { ac, and ab are bivalves} .  .  . | .  .  . | .    -a   .a  a  a  | /  /  / | /  ab    /  <------------ strong link on A/  ac  / | /  /  / | /  abc    / <------------ strong link on c---------------------------.  .  . | .  .  . | .  -a    . .  .  . | .  .  . | .  -a    . .  .  . | .  .  . | .  -a    .---------------------------.  .  . | .  .  . | .  -a    . .  .  . | .  .  . | .  -a    . .  .  . | .  .  . | .  -a    .`

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`h5 - wing { ac, and ab are bivalves} .  .  . | .  .  . | -a  -a    -a a  a  a  | /  /  / | /  ab    /  <------------ strong link on A/  ac  / | /  /  / | abcde*  abcde*    abcde* <------------ strong link on c ---------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .---------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .   . .  .  . | .  .  . | .  .  .* cells form an almost almost  subset `

Code: Select all
` H6 - wing  {bi vavles are 49,34: this functions as the 48 cell and 348 are reduced to a pair consisting of 48,  or 4 is solved}    {to read this the strong link is only on digit 4 }.  .  . | .  .  . | .     -4  ./  49  / | /  /  / | /  48    /.  .  . | .  .  . | .     -4 .------------------------------.  .  . | .  .  . | .    -4  ..  34  . | .  .  . | .  348    ..  .  . | .  .  . | .     -4  .------------------------------.  .  . | .  .  . | .     -4  . .  .  . | .  .  . | .    -4  ..  .  . | .  .  . | .   -4   . `

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`  H6b w.t.f. - wing       {to read this the strong link is only on digit 4 } .  .  . | .  .  . | -4  -4    -4 /  49  / | /  /  / | 456789~  456789~   456789~ .  34  .| .  .  . | 3456789*  3456789*  3456789*------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .------------------------------.  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    . .  .  . | .  .  . | .  .    .`

H4 example
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`+------------------------------------------------------------------------+ |  2345   8      345    |  56     26     1      |   25-4   7      9      | |  245    6      7      |  589    29     589    |   125-4  14     3      | |  259    19     159    |  4      3      7      |   6      8      25     | |-----------------------+-----------------------+------------------------| |  458    3      145    |  568    47     2568   |   9      14     12478  | |  7      2     b49     |  3      1      89     | xa48     5      6      | |  4589   149    6      |  589    47     2589   |   1278-4 3      12478  | |-----------------------+-----------------------+------------------------| |  39     79     8      |  2      5      4      |   137    6      17     | |  6      47     2      |  1      8      3      |   57-4   9      457    | |  1      5     c34     |  7      69     69     |  d348    2      48     | +------------------------------------------------------------------------+ # 79 eliminations remain H4-Wing:  (X)a = (X)b - (X=Y)c - (Y=ZX)dx     no known restrictions on "a" and "dx" cell locations (here, "x" == "a" makes for an interesting pattern) 4r5c7 = r5c3 - (4=3)r9c3 - (3=48)r59c7  =>  -4 r1268c7 `

h1 example
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`H1 - wing     .-----------------.-----------------.----------------.    | 13     5    13   | 28   278   278  | 9    6     4   |    | 4      6    7    | 9    1     5    | 2    8     3   |    | 9      2    8    | 3    6     4    | 1    7     5   |    :------------------+-----------------+----------------:    | 13568  4    2    | 18-5 3789  1789 | 568  59    689 |    | 13568  389  1359 | 4    389   189  | 568  2     7   |    | 58     7    59   | 258  289   6    | 3    4     1   |    :------------------+-----------------+----------------:    | 7      89   6    | 18   5     3    | 4    19    2   |    | 358    389  3459 | 6    2489  1289 | 7    1359  89  |    | 2      1    3459 | 7    489   89   | 568  359   689 |    '------------------'-----------------'----------------' hybrid wing (type 1): 5 r4c4 -5- r4c8 -9- r7c8 -1- r7c4 =1= r4c4 => r4c4<>5`

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`H2 - wing .------------------.-----------------.----------------.| 13     5    13   | 28   278   278  | 9    6     4   || 4      6    7    | 9    1     5    | 2    8     3   || 9      2    8    | 3    6     4    | 1    7     5   |:------------------+-----------------+----------------:| 13568  4    2    | 158  3789  1789 | 568  59    689 || 13568  389  1359 | 4    389   189  | 568  2     7   || 58     7    59   | 258  289   6    | 3    4     1   |:------------------+-----------------+----------------:| 7      89   6    | 1-8  5     3    | 4    19    2   || 358    389  3459 | 6    2489  1289 | 7    1359  89  || 2      1    3459 | 7    489   89   | 568  359   689 |'------------------'-----------------'----------------'Hybrid wing type 2: 8 r7c4 -8- r1c4 -2- r1c6 =2= r8c6 =1= r7c4 => r7c4<>8`
Last edited by StrmCkr on Mon Aug 13, 2018 6:09 am, edited 11 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 947
Joined: 05 September 2006

### Re: Hybrid - Wings {work in progress}

Some do, some teach, the rest look it up.

StrmCkr

Posts: 947
Joined: 05 September 2006

### Re: Hybrid - Wings {work in progress}

updated first post.

figured out i actually missed type 1 class,

the original ones i posted are in fact type 3 and relabel them as such.

rebuilt class type 1 to correlated with the basic chain description.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 947
Joined: 05 September 2006

### Re: Hybrid - Wings {work in progress}

StrmCkr wrote:This technique is not my own, some of it was documented by udosuk, danny, ronk, and my self
however

springs_999

holds the original naming and was the first to publish documentation of these in a very long lost post on the old players forum and at that time he dubbed them " purple cows"

hey strmckr just saw this post

thanks for the fond memories *, but the hybrid wing wasn't me, that was udosuk who came up with the original idea/naming in this thread

he comes up with the pattern designs on page 2, which include the 3 main ones that you and i call types 1,2,3, as well as the m-ring (3 strong + 3 weak continuous loop pattern) which arguably shouldn't be there. there may have been other posts on the topic but presumably they got lost in the big forum crash of 2009 so couldn't find them

the "very long lost post from the old forums" was a categorisation of the patterns that have 3 strong and 4 weak inferences with their names that was posted a short time after udosuk named the hybrid wings and you named the split wing, leaving only one pattern without a name, which i dubbed the "purple cow". i reposted the catalogue here in 2010 after the forum crash and added the 4+4 patterns too with silly names (and later posted the 4+5's separately)

the purple cow is not a hybrid wing, it is this pattern
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`. . . | . . . | . . .. *---1---*---2---* .. . . | . . . | . . .------+-------+------. . . | . . . | . . .. *-------1-------*#.. . . | . . . | . . .------+-------+------. . . | . . . | . . .. . . | . . . | . . .. . . | . . . | . . .purple cow# =/= 2`

it has no bivalues but is not the same as hybrid wing 1 since the strong links aren't all joined up. i don't know what flavour of wing you guys call this pattern nowadays, i left sudoku shortly after this

your other types seem interesting, and i feel like they deserve a separate name as you can't model them with just straight aic's with no als's/branching/whatever

* and for the crushing reminder that i'll never be a carefree teenager ever again and i feel so hopelessly old. oh my god that was NINE YEARS AGO!? why does life move so fast!
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 467
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: Hybrid - Wings {work in progress}

999_Springs
OMG hes alive and well. welcome back to the community ! long time no see, thankfully you kept some links to threads i haven't been able to dig up, or find.

i've been classing and coding a lot of different short chain stuff, the only remaining reference to a purple cow shows up in xsudoku and it very closely resembles the hybrid wings i have listed in this thread.

moreover your depiction would drop it directly over the l2-wing i documented and coded

since most of the stuff died on the great crash its been tough piecing it back together from memory or some insipidity untidy notes here and there.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 947
Joined: 05 September 2006