The New Sudoku Players' Forum

by **StrmCkr** » Mon Oct 23, 2017 5:01 am

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.

Code: Select all: H1-Wing: (X)a = (X - Y)b = (Y-Z)c = (Z)d "a" and "d" in same unit; a<>Z, d<>X H2-Wing: (X=Y)a - (Y)b = (Y-Z)c = (Z)d "a" and "d" in same unit; a<>Z, d<>X H3-Wing: (X=Y)a - (Y=Z)b - (Z)c = (Z)d "a" and "d" in same unit; a<>Z, d<>X H4-Wing: (X)a = (X)b - (X=Y)c - (Y=ZX)dx no known restrictions on "a" and "dx" cell locations

Code: Select all: H1- wing . / . | . / . | . . . . A-C . | . C-A . | . . . . / . | . / . | . . . ------------------------------ . / . | . / . | . . . / AB+ / | / BC+ / | / / / . / . | . / . | . . . ------------------------------ . / . | . / . | . . . . / . | . / . | . . . . / . | . / . | . . .

Code: Select all: H1a- wing A . / | . . . | . . . A . C-A| . . . | . . . A . / | . . . | . . . ------------------------------ / . / | . . . | . . . AB+/ BC+| / / / | / / / / . / | . . . | . . . ------------------------------ / . / | . . . | . . . / . / | . . . | . . . / . / | . . . | . . .

Code: Select all: H3 - wing . . . | . . . | . / . . AB . | . . . | . C-A . . . . | . . . | . / . ------------------------------ . . . | . . . | . / . . BC . | . . . | . C . . . . | . . . | . / . ------------------------------ . . . | . . . | . / . . . . | . . . | . / . . . . | . . . | . / .

Code: Select all: H3a - wing . . . | . . . | / / / . AB . | . . . | / C-A / . BC . | . . . | C C C ------------------------------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------------------------------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

Code: Select all: H2 - wing . AB . | . . . | . C-A . . . . | . . . | . / . . . . | . . . | . / . ------------------------------ . . . | . . . | . / . / B / | / / / | / BC+ / . . . | . . . | . / . ------------------------------ . . . | . . . | . / . . . . | . . . | . / . . . . | . . . | . / .

Code: Select all: H2a - wing . AB . | . . . | . C-A . . . . | . . . | . / . B B B | / / / | / BC+ / ------------------------------ . . . | . . . | . / . . . . | . . . | . / . . . . | . . . | . / . ------------------------------ . . . | . . . | . / . . . . | . . . | . / . . . . | . . . | . / .

Code: Select all: H4 - wing {48,34}: this functions as the 48 cell and 348 are reduced to a pair consisting of 48, or 4 is solved} . . . | . . . | . . -4 / 4 / | / / / | / / 48 . . . | . . . | . . -4 ------------------------------ . . . | . . . | . . -4 . 34 . | . . . | . . 348 . . . | . . . | . . -4 ------------------------------ . . . | . . . | . . -4 . . . | . . . | . . -4 . . . | . . . | . . -4

Code: Select all: h4 {grouped}- wing { ac, and ab are bivalves} . . . | . . . | . -a . a a a | / / / | / ab / <------------ strong link on A . ac . | . . . | . abc . --------------------------- . . . | . . . | . -a . . . . | . . . | . -a . . . . | . . . | . -a . --------------------------- . . . | . . . | . -a . . . . | . . . | . -a . . . . | . . . | . -a .

H4 example

Code: Select all: +------------------------------------------------------------------------+ | 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

Code: Select all: 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

Code: Select all: 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

updated: removed lots of crap that wasn't relevant

by **StrmCkr** » Sun Nov 05, 2017 2:56 am

added types: 5,5b,6,6b

by **StrmCkr** » Wed May 09, 2018 7:09 pm

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.

by **999_Springs** » Thu Aug 09, 2018 4:11 pm

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

Code: Select all: . . . | . . . | . . . . *---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!

by **StrmCkr** » Mon Aug 13, 2018 5:52 am

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.

The New Sudoku Players' Forum

Hybrid - Wings {work in progress}

Hybrid - Wings {work in progress}

Re: Hybrid - Wings {work in progress}

Re: Hybrid - Wings {work in progress}

Re: Hybrid - Wings {work in progress}

Re: Hybrid - Wings {work in progress}