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by **StrmCkr** » Sat Dec 27, 2014 12:38 am

This is not my own technique it has been on a few sites for a while, however the information for it was limited.

I built this page in hopes to standardize the L2-Wing technique.

an L2 wing is constructed using grouped or none grouped candidates from 2 digits containing a minimal of three strong-links.
{note: a 4th strong-link may be noted at a weak-link interface, this occurs from arrangement of the box's,row,cols used}

a generalized L2-wing is possible expansion removes the three strong-link restraint through the weak-link via additional strong-links on one candidate.
if these are used the designation gL- Wing is warranted.

information Ive located originally identified L2 -wings and L-3 wings; however L3 wings directly overlap another solving technique {hybrid wings} and use 3 candidates Ive excluded these types;

Code: Select all: L3-Wing: (X)a = (X - Y)b = (Y-Z)c = (Z)d "a" and "d" in same unit; a<>Z, d<>X H1-Wing: (X)a = (X - Y)b = (Y-Z)c = (Z)d "a" and "d" in same unit; a<>Z, d<>X

Which leaves only 1 scenario: the L2-wing which can be read in two directions,

L-Wing: (X)a = (X)b - (X)c = (X-Y)d = (Y)e =>> "a" and "e" in same unit; a<>Y, e<>X
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ { or } ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
L2 -Wing: (Y)e = (Y -X)d = (X)c -(x)b = (x)a =>> "a" and "e" in same unit; a<>Y, e<>X

L2-Wings are classed by two types :

Type 1: none grouped candidates {all strong links} so that any Box,Row,and Col sector can be used for any of the three strong links: for simplicity I'll only list an exemplar instead of generating all possible base type configurations.

Type 2: grouped candidates where by weakly linked candidates become strong links, so that a limited selection of combinations can be used for any of the three strong links, for simplicity I'll only list a few exemplars instead of generating all base type configurations.

Code: Select all: Type 1: None Grouped Candidates: (X)Col 2,8, (Y) Box 9 ->> -------------------------------------- | . / . | . . . | . / . | | . x . | . . . | . x . | | . / . | . . . | . / . | -------------------------------------- | . / . | . . . | . / . | | . / . | . . . | . / . | | . / . | . . . | . / . | -------------------------------------- | . / . | . . . | / xy+ / | | . x-y . | . . . | / / y-x | | . / . | . . . | / / / | --------------------------------------

Code: Select all: Type 2: Grouped candidates (X)Col 2,3 (Y) Col 3 Type 2a: Grouped Candidates (X) Box 6,Row 1 (Y) Col 4 -------------------------------------- ---------------------------------- | . x x | . . . | . . . | | / / / | xy+ / / | x / / | | . x x | . . . | . . . | | . . . | / . . | . . . | | . x x | . . . | . . . | | . . . | / . . | . . . | -------------------------------------- ---------------------------------- | . / / | . . . | . . . | | . . . | / . . | x / / | | . / xy+ | . . . | . . . | | . . . | / . . | x / / | | . / / | . . . | . . . | | . . . | y-x . . | x x-y / | -------------------------------------- ---------------------------------- | . / y | . . . | . . . | | . . . | / . . | . . . | | . x-y y | . . . | . . . | | . . . | / . . | . . . | | . / y | . . . | . . . | | . . . | / . . | . . . | -------------------------------------- ----------------------------------

Code: Select all: Type 2b: Grouped candidates (X) Row2,8 (Y)Box 1 ---------------------------------- | . . . | / y / | . . . | | / / / | / y xy | / x / | | . . . | / y / | . . . | ---------------------------------- | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | ---------------------------------- | . . . | . . . | . . . | | / / / | / x-y / | / x / | | . . . | . . . | . . . | ----------------------------------

Thanks to daj95376, for information examples and exemplars regarding this technique.

by **StrmCkr** » Sat Dec 27, 2014 9:18 pm

reserved for minimal examples:

L wing found after basic techniques are applied and its application reduces the puzzle to singles only:

Code: Select all: 9...5..3.4..1..9.8..6.9.4.2...97..2...42168...9..3....8.3...2..7....9.8..49.8...6

{Type 1} L-Wing: (4)r6c4 = (4-6)r1c4 = r1c7 - r2c8 = (6)r6c8 => r6c8<>4
{Type 1} L-Wing: (4)r6c4 = (4-6)r1c4 = r2c5 - r2c8 = (6)r6c8 => r6c8<>4
{Type 2a} L-Wing: (4)r6c4 = (4-6)r1c4 = r1c7 - r46c7 = (6)r6c8 => r6c8<>4

{ if you happen to have examples of this technique feel free to pm me the grid's and ill add it to this list}

Non - minimal examples

Code: Select all: ...3.2.7.7..9....5..6...4...948.....2.1...5.7.....198...8...7..4....5..3.6.2.9...

{Type 1} L-Wing (5)r6c4 = (5-7)r3c4 = r8c4 - r8c2 = (7)r6c2 => r6c2<>5
{ Type 2b} L-Wing (6)r12c5 = (6-8)r2c6 = r2c7 - r8c7 = (8)r8c5 => r8c5<>6

by **denis_berthier** » Mon Dec 29, 2014 6:02 am

Hi StrmCkr

Your L-Wing example patterns can be seen as 3D bivalue-chains[3] or whips[3]:

{Type 1} L-Wing: (4)r6c4 = (4-6)r1c4 = r1c7 - r2c8 = (6)r6c8 => r6c8<>4
is a bivalue-chain[3]: c4n4{r6 r1} - r1n6{c4 c7} - c8n6{r2 r6} ==> r6c8 ≠ 4

{Type 1} L-Wing: (4)r6c4 = (4-6)r1c4 = r2c5 - r2c8 = (6)r6c8 => r6c8<>4
is a bivalue-chain[3]: c4n4{r6 r1} - b2n6{r1c4 r2c5} - c8n6{r2 r6} ==> r6c8 ≠ 4

{Type 2a} L-Wing: (4)r6c4 = (4-6)r1c4 = r1c7 - r46c7 = (6)r6c8 => r6c8<>4
is a whip[3]: c4n4{r6 r1} - r1n6{c4 c7} - b6n6{r4c7 r6c8} ==> r6c8 ≠ 4, where n6r4c7 is a t-candidate in the 3rd cell

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L2 - Wings: examples and exemplar {2 digit - 3 strong links}

L2 - Wings: examples and exemplar {2 digit - 3 strong links}

Re: L - Wings: examples and exemplar {2 digit - 3 strong lin

Re: L - Wings: examples and exemplar {2 digit - 3 strong lin

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